Open one tube of dough and unroll onto a lightly floured clean work surface. Lightly dust the top of the dough and a rolling pin with flour and roll the dough to a 12-by-14-inch rectangle, about 1/8 inch thick. Roll out the second tube of dough to the same size and thickness.
Place the cheese slices in a single layer over one rectangle of dough. Put the second rectangle of dough on top of the cheese slices and roll with the rolling pin to seal. Fold the right side of the dough over one-third of the way to the center, and do the same with the left side to tri-fold the dough. Roll the dough back out to a 6-by-10-inch rectangle about 3/8 inch thick. Using a 3-inch donut cutter or 3-inch round cutter with a 1-inch round hole, cut out 4 donut shapes from the dough.
Pour enough oil in a heavy-bottomed Dutch oven to come 3 inches up the sides. Heat over medium-high heat until a deep-fry thermometer inserted in the oil registers 340 degrees F. Fry the donuts in batches until golden brown, about 1 minute per side. Drain on a wire rack-lined baking sheet.
In a small bowl, mix together the Dijon mustard and honey until well combined. Use a pastry brush to brush the tops of the donuts with the honey mustard and sprinkle with the chopped bacon. Serve immediately.