Boil potatoes in salted water 15-18 minutes until tender; drain and steam-dry in the hot pot.
Mash potatoes with warm milk, butter, salt, and pepper; fold in cheddar.
Brown onion, garlic, and beef in olive oil over medium-high heat, 8-10 minutes; drain fat if needed.
Stir in flour, tomato paste, Worcestershire, and thyme; add broth and simmer 5-7 minutes until thick.
Stir in frozen vegetables; cook 3 minutes; season to taste.
Spread filling in an oven-safe skillet or 9x13 dish; top with mash, seal to edges, and fork-ridge the surface.
Bake at 400°F for 20-25 minutes until bubbling and golden (broil 2-3 minutes for extra crispness). Rest 10 minutes.