Instructions

1. On large holes of a box grater, shred potatoes into a large bowl filled with cold water. Stir until water is cloudy, then drain. Cover potatoes with more fresh cold water. Stir to remove excess starch. Drain potatoes and spread on a clean tea towel. Roll up the tea towel with potatoes and squeeze out any excess moisture.
2. Mix potato shreds with onion, peppers, and jalapeño, paprika, and cayenne, if using.
3. In a 12-inch (30 cm) non-stick skillet, heat butter and oil over high heat. Sprinkle potato mixture into the skillet evenly. Cook until potatoes form a brown crust on the bottom (about 5 minutes); stir. Cook until potatoes are browned all over (about 15 minutes), stirring occasionally. Season with salt and pepper to taste.
4. Reduce heat to low; with the back of a spoon, make 6 evenly spaced wells in the potato mixture. Crack an egg into each well. Cover and cook until whites are set, 6 to 10 minutes. Remove from heat and sprinkle with cheese. Serve!