In a large bowl, whisk together the flour and salt. Add the cold butter and pinch it into the flour with your fingers or a pastry cutter until the mixture resembles coarse crumbs.
Gradually add cold water, mixing until a soft dough forms. If needed, add a touch more water, one tablespoon at a time. Knead briefly on a lightly floured surface, just until smooth.
Wrap the dough in plastic and refrigerate for at least 30 minutes while you prepare the filling.
In a skillet, heat olive oil over medium heat. Add onion and bell pepper and sauté until softened, about 4–5 minutes.
Add shredded chicken, cumin, smoked paprika, coriander (if using), and salt and pepper to taste. Stir and cook for 2–3 minutes to blend flavors. If you’re using peas, fold them in now and cook until just heated through. Remove from heat and let the filling cool slightly.
Roll the dough on a lightly floured surface to about 1/8-inch thickness. Cut rounds using a 4-inch cutter (or a cup). Re-roll scraps as needed.
Place a heaping teaspoon of filling in the center of each round. Fold dough over to form a half-moon and crimp the edges with a fork to seal.
Place formed empanadas on a parchment-lined baking sheet. Brush the tops with beaten egg for shine.
Bake in a preheated 400°F (205°C) oven for 18–22 minutes, until the crusts are golden brown and crisp.
Let them rest for a few minutes before serving. Enjoy warm with your favorite dipping sauce or salsa.