Toss the potatoes with the granulated garlic, paprika, cayenne and some salt and pepper in a medium bowl.
Add half of the butter and half of the oil to the skillet. Let melt, and then add the potatoes, pressing them down with a spatula. Cook until crisp and golden brown on one side, 5 to 7 minutes.
Set a baking sheet or a large plate over the skillet and carefully invert the potatoes onto the baking sheet. Add the remaining butter and oil to the skillet and slide the potatoes back in, un-cooked side down, and cook until golden and crispy on the second side as well, 4 to 5 minutes.
Slide onto a cutting board and cut into wedges to serve.