Preheat the oven to 400°F.
Toss diced potatoes with olive oil, garlic powder, cayenne pepper, 1/2 the salt, and black pepper. Spread on a baking sheet and roast for 40 minutes, stirring halfway through until golden and crispy.
In a bowl, whisk together eggs, milk, remaining salt, and pepper.
Heat a non-stick skillet over medium heat, add eggs, and scramble until just set.
Divide roasted potatoes and scrambled eggs among two bowls.
Top each bowl with shredded cheddar cheese and allow it to melt from the heat of the potatoes and eggs.
Serve each bowl with ketchup or Worcestershire sauce if desired.