Preheat oven to 400 degrees. Wash, but do not peel potato. Microwave on high for 1:30. Cut potato lengthwise into 6 - 8 wedges.
Combine oil, salt, cayenne pepper, and garlic in a bowl. Add potato wedges and toss to coat. Remove garlic clove and arrange on baking sheet or iron skillet, flesh side down. Place in oven and cook for 10 to 15 minutes, turning once midway when potatoes brown.
5 minutes prior to potatoes being done, heat a skillet and melt the butter until it begins to bubble. Fry the egg until desired doneness (the runnier, the better). Add salt if desired.
Remove potatoes from oven and arrange neatly on a plate so egg will cover the wedges. Place egg over wedges. Use a micro-plane or cheese grater to grate bottarga over egg and serve immediately.