In a heavy-duty skillet, heat 3 tablespoons of olive oil over medium-high heat. Add the onions and a generous pinch of salt. Reduce heat to medium and cook, stirring often, until well browned, about 20-30 minutes. Let cool.
In a large bowl, combine the caramelized onions, mashed potatoes, cheese, and chili powder, if using. Season with salt and pepper, to taste.
Spoon about 2 tablespoons of the filling to half of each tortilla and spread to the edges. Fold the tortilla over and secure with a toothpick, if necessary. Repeat until all tortillas are filled.
Fill a large skillet with enough oil to reach 1 inch in depth and heat over medium-high heat. Fry tortillas on both sides until golden brown and crispy, about 1-1½ minutes per side. Drain on a paper towel.
Serve immediately with sour cream, salsa, hot sauce, or chopped cilantro, if desired.