Place a baking sheet on rack in the lower third of the oven. Preheat oven to 400 degrees F (200 degrees C).

Heat oil and butter together in a large saucepan over medium heat; cook and stir onion until softened, about 10 minutes. Add beef; cook and stir until browned on all sides, about 5 minutes. Add garlic; cook and stir until fragrant, about 1 minute.

Stir flour, pepper, and salt into beef mixture; cook and stir until beef is coated, 2 to 3 minutes. Add wine; bring to boil, reduce heat, and simmer, 3 to 5 minutes.

Mix beef stock, potatoes, carrots, tomato paste, and Worcestershire sauce into beef mixture; bring to a boil. Reduce heat and simmer until vegetables are tender, 30 minutes to 1 hour. Remove from heat and cool.

Line a 9x13-inch baking dish with 1 pie crust. Spoon beef and potato filling into crust; top with remaining pie crust, crimping the 2 crusts together around the edges using a fork or your fingers. Brush top crust with milk.

Place baking dish on the baking sheet in the oven and cook until crust is golden brown, 40 to 45 minutes.