Preheat your oven to 375°F (190°C).
If using a homemade pie crust, roll the dough out to fit a 9-inch pie plate. Gently place the crust into the pie plate, trim any excess, and crimp the edges.
In a medium skillet over medium heat, sauté the red onion in olive oil until translucent, about 3-4 minutes.
Add the chopped sun-dried tomatoes and sliced Kalamata olives to the skillet, and sauté for an additional 2 minutes. Remove from heat and let cool slightly.
In a large mixing bowl, whisk together the eggs, heavy cream, oregano, salt, and black pepper until well combined.
Stir in the crumbled feta cheese and grated Parmesan, then add the sautéed onion, sun-dried tomatoes, and olives.
Pour the filling into the prepared pie crust, smoothing out the top with a spatula.
Bake in the preheated oven for 40 to 45 minutes, or until the quiche is set and the top is golden brown.
Allow the quiche to rest for at least 10 minutes before slicing.
Serve warm, garnished with fresh basil leaves if desired.