Preheat the oven to 200°C (392°F).
Place the red bell peppers on a baking sheet and bake until the skins are slightly blackened.Transfer the peppers to a freezer bag to cool. Grill the eggplant slices with a little olive oil until golden brown and cooked through.
Once cooled, peel the peppers, remove the seeds, and cut them into strips.
In a large bowl, whisk the eggs and season with salt and pepper.
Add half of the grated Emmental (or Fontina) cheese, Parmesan cheese, and chopped parsley.
Heat olive oil and butter in an oven-safe skillet over medium heat.
Add the grilled eggplant and roasted pepper strips.
Pour the egg mixture over the vegetables and cook until the edges begin to set.
Sprinkle the remaining cheese on top, then increase the oven temperature to 240°C (464°F).
Bake for 10 minutes, or until the frittata is golden and fully set. Serve warm and enjoy!