In a large bowl, combine flour and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs.
Gradually add ice water, one tablespoon at a time, mixing until the dough just comes together. Do not overmix.
Form the dough into a disc, wrap in plastic wrap, and chill for at least 30 minutes.
On a lightly floured surface, roll out the dough into a 12-inch circle. Carefully transfer the dough to a 9-inch pie plate. Trim and crimp the edges as desired.
In a separate bowl, whisk together the eggs, heavy cream, and milk. Season with salt and pepper.
Scatter the cooked chicken, cheddar cheese, and chopped onion evenly over the bottom of the pie crust.
Pour the egg mixture over the chicken and cheese.
Bake for 40-50 minutes, or until the quiche is set and the top is golden brown. A knife inserted near the center should come out clean.
Let the quiche cool for 10 minutes before slicing and serving.
Notes
For an extra layer of flavor, you can add a tablespoon of Dijon mustard to the egg mixture.