Season beef Chuck Roast cubes with salt and black pepper to taste. Heat oil in a large stockpot over high heat. Sear cubes in small batches, careful to not over-crowd the pan, until brown on each side, about 5 to 6 minutes. Remove cubes from pan and set aside.
Turn heat down to medium; add onions, mushrooms, and garlic to the pot and cook until lightly browned, about 4 to 5 minutes.
Pour beer into the pot and stir, scraping up and dissolving any browned bits of food into the liquid. Stir in tomato paste, thyme, and remaining vegetables. Add back in beef cubes and enough beef broth to cover all ingredients, about 3 to 4 cups. Season with salt and pepper to taste.
Bring stew to a gentle simmer, stirring to combine; reduce heat to low and cover pot with tight-fitting lid. Simmer stew until beef is fork-tender, about 2 hours, stirring occasionally.
Remove cover and raise heat to medium-high. Bring stew to a low boil and cook until stew has slightly thickened, 5 to 6 minutes. Remove from heat and add salt and pepper to taste. Garnish with parsley, if desired.