Combine olive oil, mayonnaise, lemon juice, garlic powder, kosher salt, black pepper, dried parsley, and paprika in a large bowl. Add chicken cubes and toss until fully coated. Cover and refrigerate for at least 30 minutes, up to 4 hours.
Thread marinated chicken onto metal or soaked wooden skewers, packing cubes close with no gaps between pieces.
Heat grill to medium-high, 400–450°F. Clean and oil the grates.
Combine butter, lemon juice, minced garlic, Parmesan, kosher salt, red pepper flakes, and chopped parsley in a small saucepan over low heat. Stir until melted and smooth. Split into two portions before grilling.
Place skewers over direct heat. Turn every 2–3 minutes for even char on all sides. Grill 10–14 minutes total until internal temperature reaches 165°F.
In the final 60 seconds on the grill, brush skewers with the first portion of garlic parmesan butter. Pull at 165°F and immediately coat with the second clean portion of butter off the heat. Garnish with fresh parsley and serve with lemon wedges.
