Season the chuck roast with 1 ½ teaspoons salt and 1 teaspoon pepper. Dredge in flour and shake off any excess.
Heat 2 tablespoons olive oil in a large skillet over medium high heat. Sear the roast on all sides until golden brown, about 8 minutes total. Transfer to a 6-quart slow cooker.
Add carrots, celery, onion, and garlic to the slow cooker.
In the same skillet, heat the remaining 1 tablespoon olive oil. Stir in tomato paste and cook until deep red, about 1 minute. Add flour and whisk in red wine. Pour in beef broth, bay leaves, thyme, allspice, ½ teaspoon salt, and a few grinds of pepper. Bring to a simmer and whisk until smooth, about 4 minutes.
Pour the gravy into the slow cooker over the beef and vegetables. Cover and cook on LOW for 8 hours, until the roast and veggies are tender.
Remove roast and let rest for 5 minutes before slicing against the grain. Discard thyme stems. Toss vegetables with half the parsley and season as needed. Stir remaining parsley into the gravy.
Serve sliced roast and vegetables on a platter with gravy spooned on top and extra gravy on the side.