In a large mixing bowl, whisk eggs, milk, dry mustard, red pepper flakes and salt. Add bread pieces, stirring to combine; set aside.
Heat oven to 400° F. In a large 10-inch ovenproof skillet, heat olive oil over medium high heat. Add potatoes and cook until golden and beginning to crisp. Add ham and cook, stirring often, for 2-3 minutes more. Push ham and potatoes to the side of t