In a large bowl, combine the chunks of red potatoes, minced garlic, chopped onion, diced green and red bell peppers.
Add to the vegetables the olive oil, melted butter, cayenne pepper, smoked paprika, dried rosemary, salt, and black pepper. Stir well to combine and make sure everything is coated well.
Pour the seasoning mix over the vegetables in the large bowl. Toss everything together until the potatoes and vegetables are evenly coated with the seasoning.
Spread the potato mixture evenly onto a baking sheet, separating everything as much as possible. Place in the preheated oven and bake for 25 minutes, tossing the potatoes once during the baking time to ensure even cooking.
After the initial baking, increase the oven temperature to 500 degrees F. Continue baking the potatoes for an additional 10 minutes, or until they are crisp and have developed a golden-brown color.