Drain the potatoes and pat completely dry with clean kitchen towels or paper towels. Transfer to a bowl and toss with 1 tablespoon cornstarch, 1 tsp kosher salt, and 1 tsp black pepper until evenly coated.

Heat vegetable oil in a heavy pot or deep fryer to 325°F (162°C). If you don't have a thermometer, heat until a small piece of potato sizzles gently but not vigorously.

Working in batches to avoid crowding, fry the potatoes for 3–4 minutes until just tender and pale golden (blanch stage). Use a slotted spoon to transfer fries to a paper-lined baking sheet. Do not brown fully at this stage.

Increase oil temperature to 375°F (190°C). When oil reaches temperature, fry the blanched fries in batches for 2–3 minutes more until golden-brown and crisp. Transfer to a paper-lined tray and immediately season lightly with a pinch of salt.

Cheese Sauce

While fries are finishing the second fry, make the cheese sauce. In a medium saucepan over medium heat, melt 2 tablespoons unsalted butter until foaming.

Add 2 tablespoons all-purpose flour to the melted butter and whisk constantly for 1–1.5 minutes to make a roux; do not let it brown.

Slowly pour in 1 cup whole milk while whisking to avoid lumps. Continue whisking and bring the mixture to a gentle simmer; allow it to thicken, about 3–4 minutes.

Reduce heat to low. Add 2 tablespoons softened cream cheese and whisk until smooth and incorporated.

Remove saucepan from heat and stir in 1 cup sharp cheddar and 1/2 cup Monterey Jack, a handful at a time, stirring until melted and the sauce is smooth.

Stir in 1 teaspoon Dijon mustard, 1/2 teaspoon paprika, 1/8 teaspoon cayenne, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper. Taste and adjust seasoning as needed. Keep sauce warm over very low heat, stirring occasionally. If too thick, thin with up to 2 tablespoons milk.

Assembly & Garnish

Arrange hot fries on a large serving platter or on individual plates.

Ladle the warm cheese sauce evenly over the fries, covering them generously. For extra melted cheese texture, sprinkle an additional 1/4 cup shredded cheddar over the sauced fries and place under a preheated broiler for 30–60 seconds until bubbly (optional). Watch carefully to avoid burning.

Top with optional toppings: scatter 1/2 cup chopped cooked bacon, 2 tablespoons sliced pickled jalapeños, 2 tablespoons thinly sliced green onions, and 1 tablespoon chopped fresh cilantro. Serve with 1/4 cup sour cream on the side or dotted over the fries.

Serve immediately while fries are crisp and cheese sauce is warm.