Place the mild and sharp Cheddar cheese, Worcestershire sauce, dry mustard, garlic, hot pepper sauce, and salt into a food processor; pulse a few times to finely chop ingredients. Slowly pour beer into the cheese mixture as the processor is running to make a smooth spread, about 1 minute. Transfer to a bowl, chill, and serve. The spread will firm up when chilled; if too stiff, mix in more beer, a teaspoon at a time, to desired consistency.