Preheat oven to 400°F and set a rack in the center.
Warm the olive oil in a large skillet over medium heat.
Sauté onion and carrot until softened, about 5 minutes.
Add ground beef and cook, breaking it up, until no pink remains, 6–8 minutes. Drain excess fat.
Stir in garlic and tomato paste and cook 1 minute until fragrant.
Sprinkle flour over the mixture and cook, stirring, for 1 minute.
Pour in broth and Worcestershire; simmer until thick and saucy, 3–5 minutes.
Fold in thyme and peas; season with salt and pepper. Let filling cool 5–10 minutes.
Line a 9-inch pie dish with bottom crust and spoon in the warm filling.
Cover with top crust, trim, and crimp edges. Cut a few vents on top and brush with milk.
Bake 28–35 minutes, until the crust is deep golden and the filling gently bubbles at the edges.
Rest 10 minutes before slicing so the juices settle.
Notes
Variation: Swap half the beef for ground pork, or add a handful of shredded cheddar under the top crust for a cheesy finish. Make-ahead tip: Cool the cooked filling completely, assemble, and refrigerate up to 24 hours; add 5–10 minutes to bake time. Leftovers reheat well in a 350°F oven for 12–15 minutes.This recipe is an original creation inspired by classic Easy Meat Pie Recipe flavors. All ingredient ratios and instructions are independently developed.