Place a pan over medium heat, add the butter and melt it completely.
Add the ground pepper, salt, and flour to the pan. Stir quickly to create a smooth paste.
Add the cheese and milk. Stir constantly until the sauce thickens to your desired consistency.
Roughly chop the jalapeños (or slice into rings) and stir into the sauce. Serve immediately.
Video
Notes
If you’re in a rush, you can make this sauce in the microwave. Simply add all of the ingredients together in a microwaveable jug and stir thoroughly. Cook on a high power for 3 minutes and stir again until combined. Cook for 1 minute and stir again, then repeat until the cheese sauce is thick and creamy.