Preheat oven to 400.
Combine diced potatoes, slivered onions, chopped red bell peppers, chopped broccoli, olive oil, smoked paprika, garlic powder, salt, and pepper in a medium bowl. Toss well to coat.
Arrange vegetable mixture in a single layer on a parchment-lined baking sheet. Bake at 400 for 25-30 minutes or until potatoes are soft.
Remove from oven and divide mixture evenly among 4 freezer- and microwave-safe bowls. (Oven-safe if serving immediately.) If serving immediately, reduce oven temperature to 350. If freezing, turn oven off.
While vegetables are cooking, heat butter in a medium skillet over medium heat. Crack eggs into a medium bowl. Whisk until frothy.
Cook eggs in hot skillet 4-5 minutes, stirring frequently. If freezing, leave eggs slightly undercooked. If serving immediately, cook eggs thoroughly. Divide eggs evenly among bowls, placing on top of potato mixture. Top evenly with cheese.
If freezing, cover tightly and freeze. To serve immediately, return to oven for 10 minutes to melt cheese. Top with salsa and hot sauce.
To cook after freezing, cook each bowl, uncovered, 1-2 minutes in microwave on high.