Season roast: Sprinkle roast with 2 teaspoons of the salt and 1 teaspoon of the pepper.
Add vegetables to crock: Combine potatoes, carrots, celery, onion, and garlic in a slow cooker.
Make broth mixture: Whisk together broth, flour, and tomato paste in a medium bowl; stir into slow cooker. Add thyme.
Add roast: Place roast on top of vegetables.
Cook roast and vegetables: Cook, covered, on LOW until tender, about 8 hours.
Slice roast: Transfer roast to a cutting board. Let rest 20 minutes before slicing; then cover with aluminum foil.
Remove vegetables from remaining broth: Using a slotted spoon, remove thyme and transfer vegetables to a serving platter. Sprinkle with 1/2 teaspoon of the salt. Cover with aluminum foil.
Add ingredients to gravy mixture: Whisk together Worcestershire sauce, ketchup, hot sauce, and remaining ½ teaspoon each of the salt and pepper in a bowl; stir into slow cooker.
Cook gravy until thick: Increase heat to HIGH, and cook, partially covered, until sauce thickens, 35 to 40 minutes. Serve sliced roast and vegetables with sauce; garnish with herb sprigs, if desired.