Peel the potatoes and cut them into thin fries strips using a sharp knife or mandoline for uniform thickness.
Heat vegetable oil in a deep fryer or large pot to 350°F (175°C). Carefully add the potato strips in batches, frying until golden brown and crispy, about 4-6 minutes. Use a slotted spoon to remove and drain on paper towels.
Arrange the crispy fries on a serving plate or baking sheet. Sprinkle generously with shredded cheddar cheese while the fries are still hot, allowing the cheese to melt slightly.
Add sliced jalapeños over the cheesy fries. Dollop sour cream on top or serve it on the side for dipping.
Optionally, season with salt and black pepper to taste. Serve immediately for maximum crunch and flavor.