Heat skillet (med-high) with a little oil. Add beef; break up and cook 5–6 min until browned. Drain, leaving ~1 tablespoon fat.
Add onion and carrots; cook 4–5 min until softened. Stir in garlic 30 sec.
Push mixture aside; cook tomato paste in center 1 min.
Sprinkle flour; stir to coat.
Gradually add beef stock, stirring; add Worcestershire, thyme, bay leaf; season.
Reduce heat; simmer 15–20 min until glossy and thickened. Remove bay leaf; cool slightly.
Heat oven to 400°F (200°C). Transfer filling to 9-inch pie dish. Top with puff pastry; seal, trim, and cut 3 vents. Brush with egg.
Place on baking sheet; bake 25–30 min until deep golden.
Rest 5 min for cleaner slices.
Slice and serve warm.