Grab a medium saucepan and put it on medium heat. Add 2 tablespoons of butter. Let it melt until it's almost all liquid but not browning. This takes about 1–2 minutes. I love the smell of melting butter – it's like the start of something delicious! Don't let it turn brown or it will change the flavor.
Once the butter is melted, sprinkle in 2 tablespoons of all-purpose flour. Stir it with a whisk to mix it into the butter. Keep stirring for about 30 seconds to cook the flour. You'll see it turn into a thick paste—that's your roux. It's what makes the dip nice and thick. The mixture should be smooth with no lumps.
Slowly pour in 1 cup of whole milk while whisking. Keep whisking so there are no lumps. This part can feel like a workout, but it's worth it for that smooth texture. Add the milk bit by bit at first, then faster as it mixes in. It should look creamy and even after a minute or two.
Add 1/4 teaspoon of salt and 1/8 teaspoon of cayenne pepper. Whisk them in well. The cayenne gives a little zing, but it's not too spicy. Taste and add more salt if needed. The seasoning makes all the difference in the final flavor.
Turn the heat up just a bit to bring the mixture to a gentle boil. Keep whisking as it heats up. You'll notice it getting thicker in about 2–3 minutes. It's like magic watching it turn into a sauce! Don't let it boil hard or it might curdle.
Take the pan off the heat. This is important – adding cheese to hot liquid can make it stringy. Add the 8 ounces of grated sharp cheddar cheese a handful at a time, whisking until it melts completely. This part is so satisfying—the cheese turns the sauce into a creamy, golden dream.
Your dip should be smooth and creamy now. If it's too thick, add a tiny splash of milk (like 1 tablespoon) and whisk until it's just right. It should be smooth and dippable, not runny. The perfect texture coats a spoon but still drips off easily.
Pour the dip into a serving bowl. Chop up some green onion and sprinkle it on top for a pop of color and flavor. Grab your tortilla chips and start dipping! The dip is best served warm right away.