MIX 1/2 cup sour cream and chopped chives together in a small bowl. Refrigerate.
Preheat oven to 400 degrees F. Shred 1/2 of cheese to make about 1 cup of shreds. Divide shreds into 8 piles, about 2-inches apart, on a silicone baking mat or parchment paper lined cookie sheet and bake about 5 minutes or until cheese melts and becomes crisp. Let cool 5 minutes and remove from baking sheet. Reduce oven temperature to 180 degrees F.
Cut the remaining 4 oz. cheese into 8 1/2-inch cubes. Form balls of mashed potato mixture, using an ice cream scoop. Make a small hole in center of each potato ball and fill with one cube Borden® Cheese. Cover with additional mashed potato so cheese is hidden inside. Refrigerate until ready to fry.
Heat oil in a large saucepan over medium-high heat to 375 degrees F. Prepare beer batter according to package directions; dip each mashed potato ball into batter, and deep-fry for about 5 minutes or until golden brown. Remove from oil, and drain on paper towel. Reheat oil to 375 degrees F between batches. Keep potato puffs warm in the holding oven.
Place potato puff on a plate; top with dollop of chive cream, a few chives and the Cheddar crisp. Serve immediately.