1. Place rack in lowest position of oven; preheat to 400ºF. Line a baking sheet with foil.
2. Warm oil in a skillet over medium-high heat. Cook beef, breaking up large pieces with a wooden spoon, until no longer pink, about 5 minutes. Remove to a bowl using a slotted spoon. Drain all but 1 Tbsp. fat from skillet. Add onion, carrots and celery; sauté until beginning to brown, about 5 minutes. Add garlic; sauté 1 minute. Transfer to bowl with beef; stir in Worcestershire, tomato sauce and Cheddar. Season with salt and pepper. Let cool slightly. Beat egg in a bowl with 1 tsp. water.
3. Roll out 1 sheet of pastry and fit into a 9-inch pie plate (use aluminum or tempered glass if you intend to freeze). Place on lined baking sheet. Add meat mixture and spread evenly. Roll out second sheet of pastry; place on top of pie. Fold top crust over bottom crust; crimp edges to seal. Brush top with egg wash. Cut steam vents in top.
4. Bake for 15 minutes. Reduce oven temperature to 350ºF; bake until crust is golden and filling bubbles at steam vents, 20 to 25 minutes longer.
Make it ahead
TO FREEZE: Let cool completely. Cover in plastic wrap and freeze. Cover in foil and place back in freezer.
TO SERVE: Unwrap, place pie on a baking sheet and bake at 400°F until heated through, 40 to 45 minutes.