Grate the Emmentaler cheese finely into a bowl. Add the sunflower seeds, double cream cheese, and lemon zest. Mix well. Wash the parsley and chives and pat dry. Strip the parsley leaves from the stalks and chop finely. Chop the chives into thin pieces. Mix the herbs into the cheese mixture and season with salt and pepper to taste.
Wash the chicken breast fillets and pat dry. Flatten each fillet slightly to an even thickness. Season with salt and pepper on both sides.
Heat 3 tablespoons of oil in a large skillet over medium-high heat. Fry the chicken for 3 minutes on each side until lightly golden.
Preheat your oven's grill (broiler) to high. Transfer the chicken to an ovenproof dish and spread the cheese-herb mixture evenly over each fillet, pressing down firmly.
Place under the grill and cook for 3-4 minutes until the topping is golden brown and the chicken reaches an internal temperature of 74°C (165°F).