Place an oven rack on the center shelf and preheat the oven to 300 degrees F.
Heat a Dutch oven or large saucepan over medium-high to high heat. Season 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 (I did).
Have a small cup of water nearby. Add a thin coating of oil to the pan. When the pan is barely starting to smoke, add the brisket and sear on both sides until brown, around 3 minutes per side. Repeat with the other half of the brisket if searing two pieces, adding more oil to the pan as needed. If the brown bits on the bottom of the pan look like they might burn after searing the first piece, deglaze the pan with a couple tablespoons of water before adding the remaining brisket, scraping up the brown bits with a spatula. Use kitchen tongs to transfer the meat to a large plate or cutting board. Adjust the heat to medium-low.
Add the onions, celery, and carrots to the pan along with a pinch of salt. Stir, 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. Add the garlic and cook for another minute.
Puree the tomatoes, vinegar, orange juice, and brown sugar in a blender (you can also whisk them in a large bowl, just make sure the brown sugar doesn't clump).
Add 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 (it's fine if the meat sticks out a bit). Turn the heat to high and bring the liquid to almost a boil, then cover the pot, and place in the oven.
Cook 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).
Place a colander or fine mesh strainer over a large bowl. Strain the sauce, then use a spatula to lightly press on the solids, which will extract more of the flavorful liquid. Discard the solids (see notes).
Wipe 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, around 20 minutes.
While the sauce is reducing, slice the brisket against the grain into thin slices. Place in a serving dish.
Remove from the heat. If there's any fat visible on top of the sauce, use a spoon or paper towel to remove it. Then whisk in the butter and season with salt and pepper to taste (I used around 1/4 teaspoon of each). How much you need will vary depending on how thoroughly the meat was seasoned before searing.
Pour the sauce over the brisket and serve!
Store leftovers in an airtight container in the refrigerator for up to 5 days.