Preheat your oven to 400°F and line a large sheet pan with parchment paper for easy cleanup.
Place the cubed sweet potatoes, diced bell peppers, and red onions on the pan, then drizzle with olive oil and sprinkle with smoked paprika, garlic powder, salt, and pepper.
Toss the vegetables thoroughly to ensure an even coating of oil and spices, then spread them out in a single layer to ensure they roast rather than steam.
Roast for 20 minutes, or until the sweet potatoes are fork-tender and starting to brown at the edges.
Remove the pan from the oven, stir in the rinsed black beans, and create three small wells in the vegetable mixture.
Carefully crack one egg into each well and return the pan to the oven for 5 to 8 minutes until the whites are set but the yolks remain runny.
While the eggs cook, whisk together the Greek yogurt, chopped cilantro, and lime juice in a small bowl until smooth.
Serve the hash warm with a generous dollop of the zesty yogurt sauce over the top.