In a medium saucepan, melt the butter over medium heat.
Add the diced jalapeño and grated garlic, and sauté for 1-2 minutes, until fragrant.
Sprinkle in the flour and cook, stirring constantly, for another 1 minute, until lightly golden brown.
Gradually pour in the beer, whisking continuously to prevent lumps from forming.
Add the milk, then stir in the Dijon mustard, smoked paprika, salt, and pepper.
Cook over medium heat for 3-4 minutes, until the sauce has slightly thickened.
Gradually add the grated cheddar cheese, stirring continuously until melted and smooth.
Cook for another 2 minutes, until the sauce is completely smooth and creamy.
Remove from heat and serve warm with nachos, french fries, or grilled meats.
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