Cut the smoked cheddar and smoked gouda into 1-inch chunks so they process evenly.
Place the cheese chunks in a food processor and pulse until they are broken into fine crumbs.
Add the sour cream, 1 tablespoon granulated sugar, garlic powder, and crushed red pepper to the processor.
Process until the mixture is completely smooth, stopping to scrape down the bowl as needed.
Taste and add the remaining tablespoon of sugar if you prefer a slightly sweeter spread; pulse briefly to combine.
Scoop the smoked cheese spread into a serving bowl and serve with bread, crackers, or cut vegetables, or refrigerate until ready to serve.