Melt the butter in a small saucepan over medium heat.
Add the flour and cook for 1 minute, stirring constantly with a spatula.
Whisk in half of the milk (about ¼ cup) and cook until slightly thickened.
Gradually add the rest of the milk and cook until a creamy sauce forms, about 1-3 minutes.
Turn heat to low and stir in the cheese until melted and smooth.
If the dip is too thick, add up to 2 tablespoons more milk to adjust consistency.
Season with salt, cayenne pepper, and paprika (optional), to taste.
Notes
Best served immediately. For reheating, warm in a small bowl in the microwave or in a saucepan on the stove. Stir in a little milk if needed to smooth it out.