Toss shrimp with ⅜ teaspoon kosher salt. Let sit for 15 to 30 minutes.
In a small bowl, combine butter and honey. Microwave until melted, 30 to 60 seconds.
Stir in garlic paste and red pepper flakes. Let cool slightly, about 5 minutes.
Adjust oven rack to 4 inches below broiler and preheat broiler. Line a rimmed baking sheet with foil and place a wire rack inside.
Pat shrimp dry and return to the bowl. Toss with butter mixture to coat evenly.
Arrange shrimp in a single layer on the rack.
Broil until opaque and lightly charred, about 3 to 5 minutes.
Transfer to a platter and serve with lemon wedges.