Make the crust dough: In a bowl, whisk the gluten-free flour, salt, and sugar. Cut in the cold butter with a pastry cutter or your fingertips until you see pea-sized bits. In a small bowl, whisk the egg, ice water, and vinegar. Drizzle over the flour and toss until the dough holds together when pressed.

Chill the dough: Divide into two discs (for top and bottom, or use one thicker disc for a top-only crust). Wrap and refrigerate at least 45 minutes. Cold dough is key for flakiness.

Sauté the vegetables: Melt butter in a large skillet over medium heat. Add onion, celery, and carrots. Cook 6–8 minutes until softened. Stir in garlic and cook 30 seconds.

Build the sauce: Sprinkle the gluten-free flour over the vegetables. Stir for 1 minute to coat. Slowly whisk in chicken broth, then milk. Add thyme, rosemary, and bay leaf. Simmer 5–7 minutes, stirring, until thick and glossy.

Add chicken and peas: Stir in chicken and peas. Season with salt and pepper. Remove bay leaf. Add parsley if using. Let the filling cool slightly so it doesn’t melt the crust.

Preheat and prep: Heat oven to 400°F (200°C). Grease a 9-inch pie dish or a 2–2.5 quart baking dish.

Roll the crust: On a sheet of parchment lightly dusted with gluten-free flour, roll a disc into a 12-inch round. Gluten-free dough can be delicate—use the parchment to help transfer. If using a bottom crust, fit it into the dish and trim the excess.

Fill and top: Spoon the filling into the crust-lined dish. Roll the second disc to cover the pie. Lay it over the top. Trim, tuck, and crimp the edges to seal. Cut 4–5 small slits for steam. Brush with egg wash and sprinkle with flaky salt if you like.

Bake: Place the pie on a baking sheet to catch drips. Bake 35–45 minutes, until the crust is golden and the filling bubbles at the edges. If the edges brown too quickly, tent them with foil.

Rest and serve: Let the pie rest 15–20 minutes before slicing. This helps the filling set and makes cleaner slices.