Poke holes all over the potatoes with a fork. Microwave on high for four minutes, or until partially cooked through but not to soft. Cooking time may need to be adjusted for your microwave. Let cool for a few minutes, then dice the potatoes into 1/2 inch by 1/2 inch cubes.
Add the oil to a skillet over medium heat. When hot, add the potatoes, bell pepper, onion, and garlic. Season the potatoes veggies with the salt, black pepper, cayenne pepper, and paprika and toss to combine.
Press the potatoes and veggies into a single, packed layer and cover. Let cook for 4-5 minutes, then flip the potatoes. Cover again and cook for another 3-4 minutes. Repeat this process until potatoes are browned and soft. Remove to serving plates.
Without washing the skillet, add the butter. Crack eggs into a separate bowl. When the butter has melted, pour the eggs into the skillet. If you’re skillet is big enough, do all four, if not do them two at a time. Season with salt and pepper. Cook until whites are set, then flip and cook for another 10-45 seconds, depending on how runny you prefer the yolk. Top the potatoes with the fried eggs.