Pat the beef brisket dry with paper towels and trim any very thick or hard pieces of fat, leaving a thin layer for flavor.
In a small bowl, combine the kosher salt, black pepper, smoked paprika, garlic powder, onion powder, and dried thyme to make a spice rub.
Rub the spice mixture evenly over all sides of the brisket, pressing gently so it adheres well to the meat.
Heat the olive oil in a large skillet over medium-high heat.
Sear the brisket in the hot oil for 3–4 minutes per side, until deeply browned all over, then transfer the brisket to the crock pot.
Add the sliced yellow onion to the same skillet and cook for 3–4 minutes, stirring, until starting to soften and pick up the browned bits from the pan.
Stir in the minced garlic and cook for 30 seconds, just until fragrant, then remove the skillet from the heat.
Scatter the cooked onions and garlic evenly over and around the brisket in the crock pot.
In a medium bowl, whisk together the beef broth, tomato sauce, Worcestershire sauce, brown sugar, apple cider vinegar, and Dijon mustard until smooth.
Pour the sauce mixture evenly over the brisket and onions in the crock pot.
Cover the crock pot with its lid and cook on LOW for 8–9 hours, or until the brisket is very tender and can be easily pulled apart with a fork.
Carefully transfer the cooked brisket to a cutting board, tent it loosely with foil, and let it rest for 10–15 minutes.
While the brisket rests, ladle about 2 cups of the cooking liquid and onions from the crock pot into a small saucepan.
In a small bowl, stir together the cornstarch and cold water until completely smooth to create a slurry.
Bring the sauce in the saucepan to a gentle simmer over medium heat, then slowly whisk in the cornstarch slurry.
Simmer the sauce for 2–3 minutes, whisking, until it thickens to a glossy gravy-like consistency, then remove from the heat.
Slice the rested brisket across the grain into thin slices, or shred it with two forks if you prefer a pulled texture.
Transfer the sliced or shredded brisket to a serving platter, spoon some of the thickened sauce over the top, and sprinkle with the chopped fresh parsley before serving.