Preheat oven to 400°F. Lightly grease a 12-cup muffin tin. Unfold thawed puff pastry on a lightly floured surface and gently roll to smooth seams. Cut into 12 squares, about 4 inches each. Press each square into a muffin cup, letting corners hang over the edges.

Melt butter in a large skillet over medium heat. Add onion and carrots and cook until softened, about 6-8 minutes. Stir in frozen peas and cook 1 minute more.

Sprinkle flour over vegetables and cook, stirring constantly, for 1 minute. Gradually whisk in chicken broth and milk. Simmer until thickened, about 3-4 minutes, stirring frequently. The sauce should coat the back of a spoon.

Remove from heat and stir in shredded chicken, thyme, and salt and pepper to taste. Let cool slightly, about 5 minutes - this prevents the pastry from getting soggy.

Divide filling evenly among pastry-lined cups, about 1/3 cup each. Fold corners of pastry toward center, overlapping slightly - they will not fully cover the filling. Brush pastry with egg wash.

Bake until pastry is deep golden and puffed, 20-25 minutes. Let cool in tin for 5 minutes, then use a small offset spatula or butter knife to lift out. Serve warm.