Pat the beef cheeks with a paper towel to ensure they’re nice and dry —this will help you get a good sear. Season them liberally with salt and pepper on both sides.
Heat the olive oil in a large (4 to 6-quart) braising pot, dutch oven, or heavy-bottomed soup pot over medium heat. When the oil just begins to smoke, sear the beef cheeks for about five minutes per side, until well browned and no longer sticking to the pot. Transfer the meat to a plate and set aside.
Add the celery, carrot, onion, shallot, and garlic to the pot. Sprinkle in the 1/2 teaspoon salt, then stir the vegetables to coat them with whatever oil and browned bits are in the pan. Cover the pan and let the vegetables sweat for about 10 minutes, until onions are translucent and softened, and just beginning to brown.
Add the wine, dijon, rosemary, and anchovies. Bring to a boil and let bubble for about five minutes, until the mixture has thickened a bit and no longer smells of alcohol.
Push the vegetables out of the center of the put, then place the beef cheeks in the middle of the vegetables. Pour in the hot beef broth — it should cover about 2/3rds of the way up beef. If you don’t have enough broth, add a little water.
Preheat the oven to 325ºF. When the braising liquid comes up to a simmer, cover and bake for about three hours, until you can cut the meat with a butter knife, but it is not falling apart. The braising liquid should have reduced down to a nice sauce. If it is still too thin once the beef is cooked, remove the beef to a serving plate and reduce the liquid on the stovetop.