How to Make It
Preheat oven to 350°F. Place oil and garlic in a small baking pan; cover with aluminum foil. Roast garlic in preheated oven until soft and light golden brown, about 40 minutes. Let cool 1 hour. Remove garlic from oil; place garlic in bowl of a food processor. (Reserve oil for another use.) Add butter to food processor, and process until smooth. Stir in salt. Let butter mixture stand at room temperature until ready to use.
While roasted garlic cools, stir together Italian dressing, mayonnaise, calamansi juice, and salt. Add shrimp, and toss to coat. Cover and refrigerate 30 minutes.
Heat a grill pan over medium-high. Remove shrimp from marinade, and discard marinade. Grill shrimp until cooked through, 1 to 2 minutes per side. Transfer shrimp to a large bowl. Add roasted garlic butter, and toss until butter is melted and shrimp are coated. Sprinkle with scallions, parsley, and paprika; toss to combine. Transfer to a serving plate.