Prepare the Potatoes. Wash the potatoes thoroughly under running water and pat them completely dry with paper towels. Cut each potato in half lengthwise. Then, slice each half into 3-4 wedges, making sure each piece is of similar thickness to promote even cooking.
Prepare the Dry Mix. In a large mixing bowl, combine the flour, paprika, garlic powder, onion powder, cayenne pepper (if using), a generous pinch of salt, and a few grinds of black pepper. Stir the mixture until well blended.
Heat the Oil. Fill a large pot or deep fryer with enough oil to submerge the potato wedges, about 2-3 inches deep. Heat the oil over medium heat to 350°F (175°C). Test the oil's readiness by dropping a small piece of bread into the oil; if it sizzles and turns golden brown within about 60 seconds, the oil is ready.
Bread. Take each potato wedge and cover it in the flour mixture until it's coated evenly. Shake off any extra flour.
Fry. Carefully place a few coated wedges into the hot oil. It's better to fry them in batches to make sure they aren't too close together. This helps to keep the oil's temperature high and the wedges crispy. Each batch should take about 6-8 minutes or until they're golden brown and crispy. Keep checking the wedges with a slotted spoon to make sure they aren't sticking together.
Drain and Serve. Use the slotted spoon to take out the wedges from the oil and put them on a plate covered with paper towels to remove extra oil. You can add some more salt to the hot wedges if you like. Serve them hot and crispy with your preferred dipping sauce right away.