1 part celery (theoretically by weight, but don't worry about it too much)
Tomato paste, just enough to coat the vegetables
Vegetable or olive oil
Salt and pepper, to taste
Cut your vegetables depending on how you'll use them: In 1-inch chunks if you're getting ready for a stock, or go ahead and chop them fine if you'll use them as a magic flavor-amping stir-in. (The finer they're cut, the quicker the cooking time. And here's a tip -- cut the celery smaller than everything else.)
In a wide, heavy pan or pot, heat about a tablespoon of oil for every pound of vegetables over medium heat until shimmering. Add the onions and stir until coated. And now begins the long dark journey into night.
Sauté onions, stirring often, until they soften and turn clear. Don't let it brown. Add carrots. Stir. You're going to be doing this a lot, so you might as well get a drink. Stir. When the carrots are starting to soften, turn the heat down to low. Stir every couple of minutes. The point of all the stirring is to make sure that none of the vegetables brown before the moisture gets really cooked out, because they'll be in the pan a long time, and you don't want to burn them. Sprinkle with just a little salt and pepper.
When the carrots and onions are richly browned and have lost a lot of volume (we're talking at least a half-hour here, and perhaps much more, depending on how much you're making), add a few spoonfuls of tomato paste, just enough to coat everything lightly. Cook, stirring, until the tomato paste is rusty, brick-colored. Sprinkle with just a little salt and pepper.
Add the celery. The celery is where this gets really annoying, because it will just give off water all night long, but you'll be able to tell because you can see the steam. Stir, a tiny bit of salt, you know how this goes. Keep cooking until the celery totally softens or everything else threatens to go from deep brown to burnt black. Give the whole mess a taste. It might be a little too much on its own to truly be enjoyable, but give it a stir into any soup, sauce or whatever else.
Francis Lam is Features Editor at Gilt Taste, provides color commentary for the Cooking Channel show Food(ography), and tweets at @francis_lam.