For crust: Pulse the flour, salt, and sugar in a food processor. Add the cubed butter and pulse a few times, until the butter is about the size of small peas. Add the ice water and pulse just until the dough comes together, adding additional water if needed.
Press the dough into a disk, wrap in plastic wrap, and chill while you make the filling.
For filling: Place the water, salt, carrots, potatoes, celery, and minced onion in a medium saucepan. Bring to a boil and simmer until the vegetables are tender. Drain - save the liquid and add enough water to make a full cup.
While the veggies are cooking, make the sauce. In a large pot, melt the butter over medium heat. Add the flour; whisk and cook for 1 minute. Gradually whisk in the water, chicken base, and milk. Bring to a boil, whisking until thick and bubbly.
Stir in the pepper, garlic powder, chicken, peas, and corn. Heat through. Taste and add salt as needed.
Preheat your oven to 400 degrees. Spray 6 10-ounce ramekins with cooking spray. Divide the filling between the cups.
Sprinkle your work surface with a bit of flour. Roll the dough out to a rectangle about 14x12". Cut circles that are about 1/2 inch larger than the tops of your ramekins.
Place a circle of dough on top of each cup. Roll in the edges of the dough and crimp it. Cut slits in the top of the pie crust.
Place the ramekins on a cookie sheet. (For easy cleanup, line it with aluminum foil first.) Bake on an upper oven rack at 400° for 25-30 minutes, or until the crust is golden brown.