Arrange a rack in the middle of the oven and heat to 425°F. Lightly oil a rimmed baking sheet or coat with cooking spray.
Place the sweet potatoes, zucchini, bell pepper, black beans, and corn in a single layer on the prepared baking sheet. Add the olive oil, garlic, chilli powder, cumin, and paprika. Season with salt and pepper and gently toss to combine.
Bake, stirring halfway through, until the sweet potatoes are tender, 15 to 18 minutes total. Remove the pan from the oven and create 6 wells in the vegetables. Gently crack an egg into each well, keeping the yolk intact; season the eggs with salt and pepper.
Return the pan to the oven and bake until the egg whites are set, 7 to 9 minutes. Serve immediately, garnished with cilantro, if desired.