These deli counter cheeses stand out for flavor, texture, and sandwich-making power. Luckily, you can buy some seriously delicious deli cheese at your local grocery store. Here are 5 deli counter cheeses, according to shoppers. “If you’re in the US, try American Cheese from the deli counter. Cooper SharpIf you want an iconic creamy deli white cheese, order Cooper Sharp at your deli counter.