Bœuf aux carottes is a classic French dish, I think, but I've found the recipe under that name in only one of my 8 or 10 French cookbooks. There seem to be quite a few other names for the same thing. Simply bœuf braisé, it being understood that carrots and onions will be in the pot with the meat. Or bœuf mode. Even bœuf à la mode (no, no ice cream with it).
Braising used to be done in a fireplace, with a special cooking pot called a braisière set right on top of the fire's glowing embers. The braisière had a tight-fitting lid with a rim around it so that you could put some of the glowing embers on top to turn it into a kind of oven. Nowadays, we cook things like bœuf aux carottes or bœuf bourguignon on top of the stove or in our oven.
To braise meat or vegetables, first you brown the main ingredients in what is called un corps gras — butter, oil, duck fat, or lard. That's called faire revenir la viande or faire revenir les légumes — to "bring them back", as Walt pointed out on his blog a few days ago. I've been thinking about that expression, and I think it means that browning is a way of bringing food back to life. The meat or vegetable was alive and then it was dead and maybe not very appetizing. Browning it in the corps gras turns it into something appetizing again. Does anybody have a better theory?
Here's how you make bœuf braisé aux carottes. Like so much of the good food in France, it's not so much a recipe as a method. As I said, first, on fait revenir des oignons, des lardons, et des morceaux de bœuf. Start by browning 2 or 3 sliced onions with a hundred grams (3 or 4 ounces) of diced bacon or ham in a stew pot. I like to use a high-sided pot so the cooking fat doesn't spatter everything in the kitchen. You can also include 3 or 4 garlic cloves, smashed and peeled, for more flavor.
When the onions and bacon are lightly browned, take them out and into the same pot put 2 to 2½ lbs. (un kilo) of beef cut into big chunks. Chuck roast is a good choice. It doesn't have to be the tenderest beef, but you want it to be tasty. Have the pot very hot, put the beef chunks into it in a single layer without crowding things too much, and let them brown really well on one side. Then turn them over and brown them on another side. Finally, just start stirring them around so that they brown more or less all over. You shouldn't have any or much liquid in the pot at all during the browning.
Now add the onions and bacon back into the pot and stir everything around again. Pour on enough white wine — red wine would turn the braise into a bœuf bourguignon instead of a bœuf mode — and stock or water to just cover the ingredients. Add salt and pepper at this point, along with some thyme, bay leaves, and maybe a little ground cloves or allspice. If you want a nice brown sauce, add a tablespoon of tomato paste, but don't overdo it. I added some dried shitake mushrooms and some green leek tops to my stew. The leek tops are just for flavor; leave them in big pieces so you can take them out of the stew at the end of the cooking time.
Let the beef and aromatic ingredients cook at a low simmer for at least an hour. Taste the sauce for flavor and seasonings, and add some more wine, water, or stock as you think necessary to keep the meat just barely covered. Meanwhile, peel and cut up half a dozen carrots weighing 1 to 1½ lbs. Add them to the pot and push them down into the liquid, again adding more liquid as needed. The carrots need to cook slowly for a long time and they will lend their vegetable sweetness to the meat. Let the pot continue to simmer for an hour or even two hours longer on a very low flame.
I think that's it. You can put some potatoes into the pot for the last 30 or so minutes of the cooking time if you want to eat the bœuf aux carottes with potatoes. Or, separately, you can cook some rice or pasta to have with it. It needs a green salad too, either before or after you eat the main course. Bon appétit and happy cooking.