Preheat the oven to 425°F and line a baking sheet with parchment paper.
Add the cauliflower and carrot to a food processor and pulse until finely chopped.
Add the chickpeas, cooked sweet potato, parmesan, eggs, garlic powder, onion powder, paprika, salt, and pepper to the food processor. Pulse several times until the chickpeas are broken down and the mixture is mostly smooth but still has a little texture. Don't over-process into a completely smooth paste.
Transfer the mixture to a bowl and stir in the breadcrumbs. Let it sit for 5 minutes. The mixture should be soft but easy to shape. If it feels too wet, add another 1-2 tablespoons of breadcrumbs.
Scoop about 2 tablespoons of the mixture at a time and shape into around 16 small nuggets. Arrange in a single layer on the prepared baking sheet and lightly brush the tops with oil.
Bake for 12 minutes, then carefully flip and bake for another 8-10 minutes, or until golden and lightly crisp around the edges.
Serve warm with ketchup, ranch, honey mustard, or your favorite dipping sauce.