Heat oven to 400ºF. Season the chicken with salt and pepper.
Heat 1 tablespoon olive oil over medium to medium-high heat. Add butter and garlic clove, and melt butter into oil. Add chicken and lightly brown 2-3 minutes per side then remove to plate.
Sprinkle chopped thyme over chicken and top each piece with a slice of cheese and then wrap with speck or prosciutto di Parma. Arrange chicken on a baking sheet and drizzle with about 1 tablespoon olive oil to lightly coat. Bake 15-20 minutes and remove; switch on broiler.
Arrange tomatoes on a baking sheet and cover them with Parm and breadcrumbs. Broil until golden, 3 minutes or so. Arrange 2 slices of broiled tomatoes on each chicken breast, garnish with torn basil and serve.