To make pastry, whisk flour and salt in a bowl. Add cold butter and use a pastry cutter until mixture resembles coarse crumbs.

Gradually add ice water, 1 tablespoon at a time, until dough just holds together. Shape into a disk, wrap in plastic, and chill 30 minutes.

Meanwhile, heat olive oil in a skillet over medium heat. Add onion and garlic; sauté until softened, about 3 minutes.

Add ground beef; cook until browned, breaking it up. Drain excess fat.

Stir in diced potato and carrot; cook 5–7 minutes until vegetables begin to soften. Add peas, Worcestershire sauce, thyme, salt, and pepper. Cook another 2 minutes. Remove from heat and let cool slightly.

Preheat oven to 400 °F (200 °C). Line a baking sheet with parchment.

Roll chilled dough on lightly floured surface to about ¼” thickness. Cut into four 6–7″ rounds.

Divide filling among pastry rounds, placing it slightly off-center. Brush edge with egg wash, fold pastry over filling to form a half-circle, and press edges to seal. Crimp with a fork or twist edge decoratively.

Place pasties on the prepared sheet, brush tops with egg wash, and cut a small vent in each top.

Bake 25–30 minutes until pastry is golden and crisp. Let rest 5 minutes before serving warm.