Rinse the leeks in a bowl of water and strain. Set aside.
In a skillet over medium heat, add the butter. When it is melted, add the leeks and season with salt and pepper. Cook until they are soft and tender, 6 to 8 minutes. Remove from the heat, stir in the thyme, and let cool to room temperature.
Roll out each pie dough round onto a clean dry surface. Using a 2 1/4-inch biscuit cutter cut 12 rounds from each dough. Gently press the rounds into each of the mini muffin tins to form mini crusts.
In a large measuring cup, whisk the cream and eggs with the pumpkin pie spice and a generous pinch of salt and pepper.
Fill each muffin cup with 1 teaspoon of the cooled leeks and top with 1 teaspoon of the cheese. Cover the filling with the egg and cream mixture. Place the muffin tins onto cookie sheets and put them into the oven. Bake until the egg mixture has set and the quiches are lightly browned, 10 to 15 minutes. Let cool for 10 minutes before turning them out onto a wire rack. Serve warm.