Combine 1/4 cup olive oil, basil, vinegar, 1 tbsp parmesan cheese, and sugar in a saucepan.

Heat the mixture over low heat to make the dressing.

Combine shrimp with the remaining parmesan cheese.

Heat butter and the remaining olive oil in a skillet.

Add the shrimp to the skillet.

Saute the shrimp until they turn pink, about 4 minutes.

Drain the cooked shrimp on paper towels.

Serve the shrimp on lettuce leaves.

Drizzle with the warm dressing.