Preheat the oven to 400 degrees F.
For the hashbrowns: Spray a baking sheet with nonstick spray. Spread the shredded potato on the baking sheet in an even layer. Sprinkle with the salt and some pepper and pour over the oil. Bake until golden and crispy, turning frequently, 10 minutes.
For the eggs: Meanwhile, spray a nonstick skillet with cooking spray and heat over medium heat. Crack the eggs into a bowl and whisk well. Stir in the roasted red peppers, and then add to the pan and scramble until cooked through, 3 to 4 minutes.
Spoon the potatoes into 2 mugs and top with the scrambled eggs. Sprinkle with the cheese and chives.