PREPARE THE FILLING: Heat extra virgin olive oil in a large skillet over medium heat. Sauté onion, carrots, and garlic for 5-7 minutes until soft.
CREATE THE SAUCE BASE: Sprinkle flour over vegetables, stirring constantly for 1 minute. Gradually pour in chicken broth, whisking smoothly to eliminate lumps. Bring to a gentle simmer.
ADD CORE INGREDIENTS: Stir in chicken, peas, thyme, paprika, salt, and black pepper. Simmer for 3-5 minutes until sauce thickens. Remove from heat and gently fold in the Greek yogurt or light cream. Let cool slightly.
CUT THE PASTRY: Preheat oven to 400°F (200°C) and grease a 12-cup muffin tin. Unroll puff pastry sheets and use a 4-inch round cutter to cut out 12 circles.
ASSEMBLE THE PIES: Press the pastry circles into the muffin cups. Spoon the chicken filling into each cup. Use pastry scraps to create small lids or lattice strips over the top, sealing the edges firmly.
BAKE TO GOLDEN PERFECTION: Brush tops lightly with the prepared egg wash and cut a small slit in each top lid. Bake for 20-25 minutes until the pastry is puffed and beautifully golden brown. Let cool for 10 minutes before removing from the tin.