Prepare Your Mixer. Add the softened cream cheese to a large mixing bowl. Using a hand mixer (or a stand mixer with a paddle attachment), beat the cream cheese until smooth and fluffy.
Add the Beer. Slowly pour in the beer while continuing to mix. Start with 3/4 cup and add more if needed for your desired consistency.
Incorporate the Cheese. Gradually add the shredded cheddar cheese, mixing until fully combined. The texture will be slightly chunky, which adds a delightful bite to the dip.
Season to Taste. Mix in the Dijon mustard, garlic powder, and smoked paprika. Taste and adjust with salt and pepper if needed.
Chill and Serve. Transfer the beer cheese dip to a serving bowl, cover, and let it chill in the refrigerator for about 30 minutes to allow the flavors to meld. Serve cold or at room temperature.