1Place an oven rack on the center shelf and preheat the oven to 300 degrees F.
2Heat a Dutch oven or large saucepan over medium-high to high heat, and add a thin coating of oil to the pan. Make sure to have a small cup of water nearby.
3Season the brisket generously on both sides with salt and pepper. (Depending on the size of your brisket and pan, you might need to cut the brisket in half.)
4When the pan is barely starting to smoke, add the brisket and sear on both sides until brown, around 3 minutes per side, adding more oil to the pan as needed. If the brown bits on the bottom of the pan look like they might burn, deglaze the pan with a couple tablespoons of water before adding the remaining brisket, scraping up the brown bits with a spatula.
5Use kitchen tongs to transfer the meat to a large plate or cutting board. Adjust the heat to medium-low.
6Add the onions, celery, and carrots to the pan along with a pinch of salt.
7Stir, scraping the brown glaze from the bottom of the pan so it coats the vegetables. Cook for 2-3 minutes, deglazing the pan with 1-2 tablespoons of water if needed.
8Add the garlic and cook for another minute.
9Puree the tomatoes, vinegar, orange juice, and brown sugar in a blender.
10Add the brisket back to the pan, along with the blender mixture, chicken stock, red wine and thyme. Stack the brisket as needed, moving the pieces around a bit so the sauce is covering them as much as possible.
11Turn the heat to high and bring the liquid to almost a boil, then cover the pot, and place in the oven.
12Cook the brisket for 3 hours (up to 3 1/2 hours), then remove the pot from the oven and set the top aside. Let it cool for several minutes, then use kitchen tongs carefully transfer the meat to a large cutting board (see notes).
13Place a colander or fine mesh strainer over a large bowl, and strain the sauce, using a spatula to lightly press on the solids to extract more of the flavorful liquid. Discard the remaining solids.
14Wipe down the cooking pot to remove any stuck vegetable bits. Add the sauce back to the pan and bring to a simmer. Simmer over medium or medium-low heat, stirring occasionally, until the sauce is reduced by around 1/3, about 20 minutes.
15While the sauce is reducing, slice the brisket against the grain into thin slices and place the slices in a serving dish.
16Remove from the heat and remove any fat visible on top of the sauce using a spoon or paper towel.
17Whisk in the butter and season with salt and pepper to taste.