Preheat the oven to 300°F (150°C). Pat the brisket dry, then season all over with kosher salt and black pepper.
Heat olive oil in a large Dutch oven over medium-high heat. Sear the brisket until well browned on both sides, about 4 to 5 minutes per side. Transfer to a plate.
Add the sliced onion to the pot and cook until softened, about 4 minutes. Stir in the garlic and cook for 30 seconds.
Add beef broth, bourbon, honey, soy sauce, apple cider vinegar, Dijon mustard, tomato paste, smoked paprika, and thyme. Stir to combine, scraping up any browned bits.
Return the brisket to the pot, spoon some sauce over the top, and cover tightly with a lid or foil.
Bake for 4 to 4 1/2 hours, or until the brisket is fork-tender. Baste once or twice during cooking if desired.
Transfer the brisket to a cutting board and rest for 20 minutes. Meanwhile, skim excess fat from the sauce and simmer uncovered on the stovetop until slightly thickened.
Slice the brisket against the grain and serve with the warm bourbon-honey glaze spooned over the top.