Preheat the oven to 350°F (175°C) and grease a 10-inch pie pan.
Grate the cheddar and Monterey Jack cheeses, then spread the shredded cheese evenly in the bottom and up the sides of the prepared pie pan so it fills at least half the pan.
In a large bowl, whisk the eggs, all-purpose flour, and half-and-half until smooth and fully combined.
Pour the egg mixture over the shredded cheese in the pie pan, distributing it evenly.
Dollop the salsa and the canned diced green chiles evenly over the top of the quiche filling.
Bake at 350°F (175°C) for 40–50 minutes, or until the filling is set and the center does not jiggle much; a toothpick inserted in the center should come out clean.
Remove from the oven and cool for 10–15 minutes before slicing to allow the quiche to finish setting.