In a food processor or bowl, combine flour, salt, and pepper. Add cubed butter and pulse (or cut in) until mixture resembles coarse crumbs.

Gradually add ice water, 1 Tbsp at a time, until dough begins to form. Gather into a ball, flatten into a disc, wrap, and chill for at least 30 minutes.

While dough chills, heat a skillet over medium heat. Add ground meat and cook until browned, breaking apart. Drain excess fat.

Add onion, carrot, celery, and garlic; sauté until softened, about 4–5 minutes. Season with thyme, salt, and pepper. Remove from heat and stir in cheese; let filling cool.

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

On a floured surface, roll chilled dough to about 1/8-inch thickness. Use a 4–5-inch round cutter (or small bowl) to cut circles.

Spoon about 2 Tbsp of filling onto the center of each circle. Brush edges with beaten egg. Fold dough over filling to create a half-moon shape and seal edges with a fork.

Transfer pies to the prepared baking sheet, brush tops with egg wash, and cut a small slit in each for steam release.

Bake for 18–20 minutes or until golden brown and crisp.

Let cool for a few minutes before serving warm.