Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
Place the garlic and parsley in the bowl of a food processor. Pulse until finely chopped. Add the ground chuck, Parmesan cheese, tomato paste, salt, and pepper. Pulse until ingredients are combined. Form the mixture into 9 patties. Place the burgers on the grill and cook for 4 to 5 minutes each side.
Brush the cut sides of each roll with the olive oil and toast on the grill for 1 to 2 minutes until slightly golden.
To serve, place 1 mini burger on the bottom half of each of the rolls. Place 1 slice of Taleggio cheese on top of the burgers. Place the basil leaf on top of the cheese and cover with the top half. Serve.