Place shredded potatoes in a large bowl full of cold water and mix them around before draining them and patting them dry.
Melt butter with oil in a flat heavy-bottomed skillet (oven proof) over medium heat. Add the cut bell peppers and onions, and sauté 3 to 5 minutes or until tender. Add garlic; sauté 1 minute.
Stir in the shredded potatoes, paprika, and 1 tsp. salt. Cook, stirring often, for about 10 minutes or until the potatoes are golden and tender.
Remove from heat. Make 6 indentations in the potato mixture using the back of a spoon.
Break 1 egg into each indentation. Sprinkle eggs with salt & pepper.
Bake at 350° for 12 to 14 minutes or until the eggs are set.
Note: Soaking the shredded potatoes in cold water keeps them from turning gray before cooking. It also rinses off some of the starch. Drain and pat them dry, so they won't stick to the cast-iron skillet.