Position 2 racks in the upper and lower thirds of the oven and preheat to 400 degrees . Trim each tortilla into an extra-large triangle by cutting a strip off two sides and leaving the bottom rounded. Brush the tortillas lightly on both sides with oil and arrange in a single layer on 2 large baking sheets. Bake until golden-brown and crisp, about 15 minutes.
Meanwhile, in a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook until lightly golden, 2 minutes. Whisk in the milk, bring to a boil, lower the heat and simmer until thickened, about 4 minutes. Stir in the cheese, a few slices at a time, until melted. Serve the jumbo chips with the cheese sauce for dipping.