Bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until mostly cooked through, 8 to 10 minutes. Add shrimp to the pot and cook until bright pink on the outside and the meat is opaque, 2 to 3 minutes; penne should be cooked through at this point.

While the penne is cooking, combine avocado, basil, 2 tablespoons Romano cheese, garlic, and lemon juice in a food processor; season with salt and pepper. Process until smooth. Add olive oil and pulse until creamy. Remove the blade from the food processor; stir diced tomatoes into pesto.

Drain penne and shrimp, then return to the pot. Add pesto, season with salt and pepper, and stir to coat.

Garnish servings with remaining Romano cheese.