Turkey Cacciatore Burgers on Portobello "Buns"

1 1/3 pounds ground turkey breast, the average weight of 1 package

Salt and pepper

6 crimini mushrooms (baby portobellos) stems removed and finely chopped

1/2 red bell pepper, seeded and chopped

1/2 yellow onion, finely chopped

2 cloves garlic, smashed away from skin and finely chopped

3 tablespoons tomato paste

1 tablespoon Worcestershire sauce

1 teaspoon crushed red pepper flakes

1/2 cup grated Parmigiano-Reggiano or Romano, a couple of handfuls

Extra-virgin olive oil, for drizzling

Handful flat-leaf parsley, chopped

4 large portobello mushroom caps, stems removed

Coarse salt and black pepper

2 cups arugula leaves, coarsely chopped

1/2 pound fresh mozzarella or fresh smoked mozzarella, thinly sliced

Sliced red onion and sliced yellow and plum tomatoes