Grilled Cajun Shrimp and Crawfish Pizza

Name: Grilled Cajun Shrimp and Crawfish Pizza
Ingredients: 1/2 stick (4 tablespoons) unsalted butter; 1 clove garlic, minced; 1 cup heavy cream; 3/4 cup grated Parmesan; 1 teaspoon Cajun seasoning; 1/4 teaspoon smoked paprika; Kosher salt and freshly ground black pepper; Pinch sugar, optional; 2 tablespoons olive oil, plus more for brushing; 1/2 pound peeled and deveined shrimp; 2 1/4 teaspoons Cajun seasoning; 1/4 cup diced red bell pepper; 1/4 cup diced yellow onion; 1/2 pound cooked peeled crawfish tails; 1 pound prepared pizza dough; All-purpose flour, for rolling; 1 cup shredded mozzarella cheese; 2 cloves garlic, minced; 1/4 cup chopped fresh parsley; Melted unsalted butter, for brushing; 1/4 cup freshly grated Parmesan