Preheat oven to 375 F. Line baking sheets with aluminum foil and spray with nonstick spray.
Open one sheet of puff pastry on a cutting board and brush lightly with beaten egg.
Sprinkle surface with 1/2 cup of cheese to evenly cover entire surface.
Dust rolling pin lightly with flour and roll over the cheese to gently press into the puff pastry.
Cut the puff pastry into long 1/2-inch wide strips. Take each strip, fold in half, pinch the ends together, and carefully twist each strip several times.
Wrap a piece of bacon around the twisted pastry and place on the baking sheet. Repeat with the remaining puff pastry and bacon.
Combine brown sugar, salt, and pepper in a pie plate and carefully dip each bacon wrapped pastry in the sugar mixture, one at a time. Place each twist back on the baking sheet and repeat with the remaining twists.
Bake the twist for 30 to 50 minutes, rotating the pan halfway through. Once the bacon is cooked, remove from oven and cool for 10 minutes.