Preheat oven to 375 °F (190 °C). Lightly grease a 12‑cup muffin tin or line with paper liners.

Heat olive oil in a skillet over medium heat. Add chopped onion and cook until softened, about 3–4 minutes. Add sausage, breaking it up with a spoon, and cook until browned and cooked through. Drain excess fat and set aside to cool slightly.

In a bowl, whisk together eggs, milk or cream, cheese, thyme, parsley (if using), salt, and pepper until well combined.

Roll out pie crusts and cut into 12 circles large enough to line each muffin cup with some overhang. Press circles into the cups, trimming excess if needed.

Evenly divide cooked sausage mixture among the crust-lined cups.

Pour egg-cheese mixture over the sausage in each cup, filling nearly to the top.

Bake for 20–25 minutes, until the crust is golden and the egg filling is set. A toothpick should come out clean in the center.

Let pies cool in the tin for 5 minutes before carefully removing. Serve warm or at room temperature.