Bring the beer to a boil in a small saucepan over high heat. Reduce the heat to low and simmer for 1 minute. Transfer to a small bowl and cool to room temperature. Process the cheddar, onion, ketchup, mustard, Worcestershire, Tabasco, and garlic in a food processor until very smooth, about 1 1/2 minutes. With the machine running, slowly drizzle in the beer and process until the mixture is smooth, about 1 minute. Transfer to a bowl, cover tightly with plastic wrap, and refrigerate until firm, about 2 hours.
To Make Ahead
The spread can be refrigerated, wrapped tightly in plastic wrap, for up to 1 week.