Adding the Tomatoes and Letting It Be, No Fussing
Here's the thing about this lesson. It's short, and that's on purpose, because the actual work you're doing today is about ten minutes long and after that your job is to leave the pot alone.
We spent last time on the browning, the onion and carrot going soft and a little golden, the timer set so nobody's pan turns into a campfire while they wander off to do something else (ask me how I know). By now your kitchen should smell like something's happening. That's the base. Everything else builds on top of it.
Adding the tomatoes
If you're using canned whole tomatoes, crush them with your hands over the pan or in a bowl first. I know that sounds messy and it is a little, but you get better texture than running them through a blender, which turns everything smooth and kind of pureed-baby-food in a way I don't love. Your hands do a rougher, better job. If canned crushed tomatoes are what you've got, that's fine too. I said jarred sauce is fine and I meant it, and canned crushed tomatoes are even less of a compromise than that. Nobody needs to apologize for a can.
Dump the tomatoes in with your browned vegetables and whatever meat you've got going. Give it a stir to bring it all together. Add a splash of water or stock if it looks too thick to move, you want it loose enough to simmer, not sitting there like paste.
Now here's the part people struggle with, and it's not a hard part, it's an emotional part. You bring it up to a bare simmer, just a few lazy bubbles breaking the surface, turn it down low, and then you walk away.
The letting-it-be part
My mother-in-law watched me cook once, years back, and told me I fuss too much. She wasn't being unkind, just accurate. I used to hover over pans like they'd misbehave if I looked away, stirring things that didn't need stirring, checking things that were fine. It's taken me a decade to learn that a ragu doing its job for twenty, thirty minutes on low heat does not need me standing over it with a spoon. It needs the lid cracked, the heat low, and a check-in every ten minutes or so, not a vigil.
So set it low. Crack the lid so some steam escapes but not all of it. Set a timer if that helps you resist the urge (it helps me). Go set the table, go help somebody with homework, go sit down for a minute. The sauce is doing the work now, and your standing over it doesn't speed anything up, it just makes you tired before dinner's even ready.
While it goes
This is a good window to taste and adjust, but not yet, not in the first ten minutes. Let the flavors start to marry before you go changing things. When you do taste, and you should, taste for salt first. Tomatoes vary a lot in acidity, some cans are bright and sharp, some are flat and need help, and your only way to know which you've got is to taste.
Which brings me to something I'll admit I resisted for a long time. My granddaughter tried a salad dressing I made once, one I'd put too much lemon in, I thought, and I served it anyway apologizing the whole time, telling everybody at the table it was probably too sharp. She said it was the best one she'd had. Kids don't flatter you to be polite, they just say what's true, so I've believed her ever since. Now if a sauce tastes a little flat to me I lean acidic before I lean sweet, a squeeze of something or an extra bit of tomato, rather than reaching for sugar to fix it, which is what a lot of recipes tell you to do. Try it both ways over time and see what you like. I could be wrong that acidic is always the fix, everybody's palate runs different, but it's where I go first now.
If the sauce tastes thin or the tomatoes taste more like tin than fruit, a small pinch of sugar can round it out, that's real, I'm not going to pretend otherwise. Just don't reach for it before you've reached for salt and acid first.
What not to do
Don't crank the heat to speed things up. A ragu at a hard boil breaks down differently than one at a low simmer, it gets harsh and can scorch on the bottom before you notice, especially if your pan is thin. Low and slow isn't a suggestion here, it's doing actual chemistry, breaking down the tomatoes and marrying the fats and building something that a fast sauce can't fake. If you're in a hurry tonight, that's a real constraint and I respect it, but this lesson is for the nights you've got the time. Jarred sauce exists for the other nights. There's no shame in that trade.
Give it at least twenty minutes on low, thirty or forty is better if you've got it, stirring only occasionally so nothing sticks. That's really the whole lesson. Not much to do. Just don't do it.
Before next time: let a pot of something simmer on low for twenty minutes without touching it more than twice, just to feel what that kind of patience is like in your own kitchen.