Mix ¾ cup natural yogurt and ¾ cup heavy cream in a medium bowl until combined with a wire whisk or spoon. Don't use an electric mixer.
Add 3 eggs and stir until well combined without beating. We don't want to beat the eggs much; we just want to combine them well.
Add ¼ teaspoon salt and ⅛ teaspoon black pepper and stir to mix. Go easy on the salt as the ham and cheese are already salty.
To assemble the quiche:
It's best to fill the quiche dough near the oven. Place the sliced ham in the bottom. Scatter both types of cheese, distributing evenly over the ham.
Slowly pour the cream mixture covering the whole surface. Don't overflow the walls of the quiche, but they will fill completely.
Bake for 35-40 minutes, until puffed and golden.
Let cool on a wire rack for a few minutes and eat. The filling will deflate and that is fine.
Eat warm or at room temperature.
Notes
Make-ahead: after removing the quiche from the oven, let it cool completely on a wire rack. Wrap in plastic and refrigerate for 2-3 days. Or freeze, well wrapped, for a month.Serving: serve it straight from the oven or at room temperature as finger food. It travels well for picnics and is amazing as part of a brunch table.Onions: lightly cooked ¼ cup yellow or green onions or scallions can be added to the filling. Also 2 tablespoons chopped chives, which are less strong. Flavorings: you can add some spice (ground jalapeños, Merken, paprika, etc) to the binding cream for a spicy kick. Or a thin layer of mustard before adding the ham.