Step 1

Prepare a grill for medium-low heat. Cook hazelnuts, sesame seeds, butter, and ¼ cup oil in a small saucepan over medium-low heat, stirring and swirling pan often, until nuts are a deep golden brown, 7–10 minutes. Remove from heat and stir in paprika, brown sugar, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 1 tsp. pepper. Finely grate in garlic; stir to combine. Set aside.

Step 2

Place leeks in a medium bowl and toss with remaining 3 Tbsp. oil and 2 tsp. Diamond Crystal or 1 tsp. Morton kosher salt; season with pepper.

Step 3

Arrange leeks, cut side down, on grate. Cover and grill, undisturbed, until deeply charred underneath, 10–15 minutes. Using tongs, turn leeks over. Cover and grill until deeply charred on other side and very soft inside (cut through one to test), 10–13 minutes.

Step 4

Transfer leeks to a platter. Drizzle vinegar over; top with sauce and nuts.