Preheat a grill pan over medium high heat. Toss the quartered fennel in 2 tablespoons extra-virgin olive oil and season with salt and pepper. Put fennel on grill and grill on all sides, approximately 2 minutes. Remove from grill and cool. Once cooled, thinly slice and reserve.
Combine lamb, rosemary, orange zest, finely chopped red onion, salt and pepper. Make 12 balls and flatten them into 3 inch meat patties. Grill 2 to 3 minutes on each side.
Combine lettuces in a shallow bowl with sliced onion. Add sliced cooled fennel to salad. Scatter the oranges and parsley around the salad. Dress with vinegar, oil, salt and pepper, to your taste. Top portions of salad with 3 mini lamb patties and serve.