Heat 1 tablespoon vegetable oil and 2 tablespoons butter in a 5–6 quart Dutch oven over medium-low heat; add sliced onions and 1 teaspoon kosher salt and cook, stirring every 5–7 minutes, until deep golden brown and softened, 40–50 minutes.

While onions cook, pat the chuck roast dry and season all over with 1/2 teaspoon kosher salt and 1/2 teaspoon black pepper (reserve remaining seasoning for later).

When onions are about 10 minutes from done, heat remaining 1 tablespoon oil in a large skillet over medium-high heat and sear the roast 3–4 minutes per side until a deep brown crust forms; transfer roast to a plate.

Add 1 tablespoon butter to the skillet, cook 30 seconds, then pour in 1 1/2 cups beef broth and scrape up browned bits; stir in 1 tablespoon Worcestershire sauce and pour this deglaze over the caramelized onions.

Nestle the seared roast into the onion bed, add thyme and bay leaf, and sprinkle the roast with the remaining 1 teaspoon kosher salt and 1/2 teaspoon black pepper.

Bring liquid to a gentle simmer on the stovetop, cover the Dutch oven, and transfer to a 300°F oven; braise until internal temperature reaches 190°F for sliceable tender beef or 200–205°F for shreddable meat, about 2 to 2 1/2 hours for a 3–3.5 pound roast.

Remove roast to a cutting board and tent with foil; rest 15 minutes.

Skim excess fat from the braising liquid, then place the Dutch oven over medium-high heat and reduce the sauce 8–12 minutes until slightly thick and glossy; taste and season with additional salt if needed and stir in 1 teaspoon balsamic vinegar if using.

Slice the roast against the grain into 1/4–1/2 inch slices, arrange on a platter, and spoon the caramelized onion sauce over the meat before serving.