Preheat oven to 375 degrees F.
In a small saucepan over medium-low heat, cook hazelnuts for 3-5 minutes, just until they start to smell fragrant.
Add sesame seeds, butter, and 2 Tbsp oil, stirring and swirling pan often, until nuts are a deep golden brown, 7–10 minutes.
Remove pan from heat. Stir in paprika, brown sugar, 1/8 tsp kosher salt, 1/2 tsp. pepper, and garlic. Stir to combine. Set aside.
Slice white and light green parts of leeks into thick coins. Gently rinse under cold water and ensure that there is not any dirt caught between the layers. Keep the slices intact as much as possible.
Very gently toss leek coins with the remaining 2 Tbsp oil and 1/8 tsp kosher salt. Roast at 400 for 15 minutes on each side.
Transfer leeks to a decorative platter, or divide between 4 small plates. Top with spiced hazelnuts.