For the pastry dough, place the flour, sugar and salt in the food processor and pulse a few times. Pour water over a cup of ice to chill. Then cut the cold butter into cubes and add to the flour. Pulse several times until the butter is cut into the size of peas. Add 3 tablespoons ice water (without the ice) and pulse again until the dough absorbs the flour and looks like soft pebbles.
Flour a work surface and dump the crumbly dough out onto the surface. Press together into a flat square, then fold toward the center into a 3-section fold. Roll the dough down to 3/4 inch and fold again in the same manner. If the dough is not coming together, sprinkle 1 teaspoon of ice water over the top and keep folding. Fold and roll the dough 3-4 times, until it is smooth. Then fold into a rectangle, wrap in plastic and chill.
Preheat the oven to 400o F and spray a muffin tin (or four 6-ounce ramekins) with non-stick cooking spray. Place a large skillet over medium heat and add the butter and onions. Sauté 2 minutes, then add the chicken pieces and garlic. Sauté another 2-3 minutes, then add the flour, herbs, and chicken base. Stir to coat. Pour in the water and cream, then stir well. Allow the mixture to come to a simmer to thicken, then add the frozen veggies. Taste for salt and pepper and add a couple of dashes of cayenne for a little kick. Remove from heat.
Now take the pastry dough out of the fridge and roll out into a 12-inch circle/square. Cut it into 4 equal triangular pieces. Then fit each piece down into the prepared muffin tin. Spread them apart—they grow! Fill the pastry dough with chicken filling, spooning in the creamy base. Then loosely fold the flaps over the top. It's okay if there are gaps in the top as long as the pastry dough sides come up high. Brush the egg wash over the top of the pastry dough. Bake for 20-25 minutes on the bottom rack, until golden brown. Allow them to cool for 10 minutes.
To serve, run a butter knife around the inside edge of the muffin tins. Tip the knife down and carefully lift each pot pie out. If you accidentally poke a hole in the pot pie, serve it in a bowl.