Bring a medium pot of salted water to a boil and add the diced potatoes. Cook until fork-tender, about 10–12 minutes. Drain well and return to the pot to steam off excess moisture.

Meanwhile, heat the butter in a large skillet over medium heat. Add the chopped onion and a pinch of salt. Cook, stirring occasionally, until the onion is soft and translucent—about 5 minutes.

Add the minced garlic, smoked paprika, and cumin to the skillet. Toast them for 30–60 seconds until fragrant.

Mash the drained potatoes in the pot, adding the sour cream or Greek yogurt if using, and season with salt and pepper.

Fold the sautéed onion and spice mixture into the potatoes until evenly combined and creamy.

Stir in 3/4 cup of the shredded cheese, cilantro, and lime juice if using. Taste and adjust seasonings.

Warm the tortillas in a dry skillet or microwave until pliable. Spoon a generous 1/2 cup of the potato mixture into the center of each tortilla, fold the sides over, and roll into a burrito.

In a clean skillet over medium heat, place the burritos seam-side down and cook until golden and crisp, about 2–3 minutes per side.

Transfer to a tray, sprinkle with remaining cheese, and let rest for a minute before serving.