In a medium bowl, combine the flour, sugar, and salt. Add the cold butter cubes and use a pastry cutter, two knives, or your fingertips to work the butter into the flour until the mixture resembles coarse breadcrumbs with pea-sized pieces of butter remaining. Add the cold sour cream and mix gently with a fork until the dough just comes together, then finish bringing it together with your hands—be careful not to overwork it or the crust will be tough. Form the dough into a flat disc, wrap it in plastic, and refrigerate for at least 30 minutes while you prepare the oven and filling.
Preheat your oven to 375°F. While it heats, lightly grease a 12-cup muffin tin with butter or cooking spray. On a lightly floured surface, roll out the chilled dough to about 1/8-inch thickness. Using a 2-inch round cutter (or the rim of a glass), cut 12 circles from the dough. Press each circle gently into the prepared muffin cups, working the dough up the sides slightly—I like to use my thumb to press from the bottom up, which helps prevent the dough from shrinking during baking.
In a medium bowl, whisk together the room-temperature eggs, heavy cream, milk, kosher salt, garlic powder, and black pepper until well combined and slightly frothy. This mixture should be smooth and homogeneous. Set aside while you prepare the ham and cheese.
Divide the diced ham evenly among the 12 prepared muffin cups, using about 1 tablespoon per cup. Sprinkle the shredded cheddar cheese over the ham in each cup, dividing it equally. Pour the egg custard mixture from Step 3 into each cup until they're about 2/3 to 3/4 full—don't overfill or the custard will overflow. Place the muffin tin in the preheated 375°F oven and bake for 15–18 minutes until the tops are golden and the centers are just set (they should jiggle very slightly when gently shaken). Let cool for 2–3 minutes in the tin before running a small knife around the edges and removing.
Transfer the warm quiche muffins to a serving platter or let them cool slightly on a wire rack if serving later. Garnish with chopped green onions if desired—they add a fresh, bright contrast to the rich, savory filling. These are delicious served warm, at room temperature, or even chilled the next day.