Microwave the baby potatoes with 2 tablespoons water for 7 to 8 minutes until fork-tender, then drain them.
Heat the olive oil on a griddle, smash the potatoes to 1/2 inch thick and season with half the salt and the smoked paprika.
Cook for 4 minutes per side until the edges are dark gold and crisp.
Whisk the eggs with the remaining salt and black pepper and scramble them in a nonstick skillet until 160°F.
Divide the potatoes, eggs and cheddar among the tortillas and roll them tightly.
Toast the wraps seam-side down for 2 minutes, then turn and toast for 1 minute more.