In a medium saucepan over medium heat, melt the butter. Whisk in the flour and cook for 1 minute until bubbly.
Gradually whisk in the milk, stirring constantly until the mixture thickens, about 2-3 minutes.
Reduce heat to low. Add the shredded cheddar cheese, chili powder, cayenne (if using), and salt. Stir until the cheese is fully melted and sauce is smooth.
Arrange tortilla chips on a platter. Pour the cheese dip over the chips or serve on the side.
Top with desired toppings and serve immediately.
Tips
For a spicier dip, add more cayenne or a dash of hot sauce.
If the sauce becomes too thick, thin with a little extra milk.
Leftover cheese dip can be refrigerated and reheated gently.