Heat broiler to high and position a rack 6-inches (15cm) from broiler.
Heat butter in a large non-stick oven-safe pan over medium heat. Add panko and chili flakes and cook, stirring occasionally until panko is lightly toasted, 2 to 3 minutes. Season with salt and pepper and set aside in a small bowl.
Score the cut side of zucchinis with a cross hatch pattern and drizzle with olive oil. Season with salt and pepper. Increase heat to medium-high and cook zucchini in pan, cut-side down, until golden, 3 to 5 minutes. Remove from heat.
Stir parmesan into panko mixture. Top scored side of zucchinis with panko mixture. Place in oven and broil until browned, checking often, about 2 to 4 minutes.