Step 1

Pulse the garlic in a food processor until finely chopped but not a paste, scraping down the sides as needed. Transfer to a large cast-iron or nonstick skillet, add the butter and cook over medium heat, stirring frequently, until the garlic is a light golden color, about 5 minutes. Be careful not to overcook the garlic or it will become bitter. Immediately transfer to a large heatproof bowl and stir in the paprika, cayenne and 1 tablespoon2 teaspoons salt. Let the garlic butter cool to room temperature, about 20 minutes. Wipe out the skillet and set aside.

Step 2

Meanwhile, combine the cabbage, scallions and cucumber in a medium bowl. Add the rice vinegar, 2 tablespoons of the oil and a generous pinch of salt; toss to combine and set aside.

Step 3

Put the shrimp in the food processor and pulse until coarsely chopped but do not puree to a paste. Transfer to the garlic butter and stir to combine. Form the mixture into 9 patties, about 1/3 cup each. Heat the remaining 1 tablespoon oil in the skillet over medium-high heat until shimmering. Add the shrimp patties and cook until golden on both sides and cooked through, about 8 minutes.

Step 4

Split the slider buns and spread the tops and bottoms with mayonnaise. Put a patty on each of the bottom buns. Top with some cabbage slaw and close the sliders with the top buns.