In a medium saucepan, melt the butter over medium heat. Be careful not to let it brown; you just want it to melt completely.
Once the butter is melted, add the flour and whisk continuously for about 1-2 minutes to form a roux.
Slowly pour in the milk while whisking constantly to prevent lumps. Continue to whisk until thickened, about 3-5 minutes.
Reduce heat to low and add the shredded Cheddar cheese. Stir until melted and smooth.
Add a pinch of cayenne, salt, and pepper. Taste and adjust seasoning as needed.
Your Easy Homemade Cheese Sauce is ready! Drizzle over dishes or use as a dip.