Wash and peel the potatoes if desired. Cut each potato into 1/4- to 1/3-inch thick sticks for classic fries. Soak cut fries in cold water for 30 minutes to remove excess starch; this helps them crisp.

Dry fries

Drain the potatoes and spread them on clean kitchen towels or paper towels. Pat thoroughly dry—any surface moisture will cause oil splatter and reduce crispness.

Heat oil

Pour about 1 cup vegetable oil into a deep skillet or medium pot (enough for a single layer or shallow fry). Heat over medium-high until oil reaches 325°F (if you don't have a thermometer, test with a small piece of potato; it should sizzle steadily).

First fry (blanch)

Fry the potatoes in batches for 3–4 minutes until pale, soft, and just starting to take color. They should not brown. Remove with a slotted spoon to a paper towel-lined tray. Allow oil to return to 375°F between batches.

Second fry (crisp)

Increase oil temperature to 375°F. Fry the blanched potatoes in batches for 2–3 minutes until golden-brown and crisp. Drain on paper towels, then immediately season with 1.5 tsp salt and 1/2 tsp black pepper while hot.

Cheese Topping

Make a quick cheese sauce (roux method)

In a small saucepan over medium heat, melt 1 tablespoon butter. Add 1 tablespoon flour and whisk continuously for about 1 minute to form a light roux (no browning).

Add milk

Gradually whisk in 1 cup milk, smoothing any lumps. Cook, whisking constantly, until the mixture thickens and coats the back of a spoon, about 3–4 minutes.

Melt cheeses

Reduce heat to low. Whisk in 2 cups shredded sharp cheddar and 1 cup shredded mozzarella in handfuls until smooth and melted. Stir in 1/2 tsp Dijon mustard, 1/4 tsp hot sauce, 1/4 tsp salt, and 1/4 tsp black pepper. Taste and adjust seasoning. Keep warm on the lowest heat, stirring occasionally.

Assemble

Arrange the hot fries on a large serving platter or divide among individual plates. Spoon the warm cheese sauce evenly over the fries so it blankets and melts into them. Alternatively, place fries on an oven-safe tray, drizzle sauce over, and broil 1–2 minutes to get a bubbling top (watch carefully).

Garnish

Scatter 2 tablespoons chopped green onions over the sauced fries and sprinkle 1/4 tsp crushed red pepper flakes if using. Serve immediately while hot and gooey.