In a glass measuring cup, add the warm water and the yeast. Stir and let sit for 10 minutes.
In a food processor fitted with a dough blade, add the dry ingredients and the Parmesan and pulse together 3 times at 5 second intervals. Add in 1 egg and the warm water and yeast mixture. Mix until the dough comes together, pulse for 10 second intervals 3 times. Turn out onto a lightly floured work surface or cutting board. Knead 10 to 12 times, adding a little flour, if sticky. Cut the dough in half and set aside.
Roll out 1 piece of dough to a 12 by 17-inch rectangle, about 1/4-inch thick. Sprinkle 3/4 cup of the Cheddar in the middle (short way). Fold 1/3 of the dough over, and sprinkle with 3/4 cup of the Cheddar. Fold the last third over and pinch the edges closed. Roll with a rolling pin to form an 11 by 15-inch rectangle. Cut into 1 1/2-inch lengthwise strips.
Pinch the cut edges together and then roll into cigar shape. Form into a pretzel shape and put on a baking sheet lined with a silicone baking mat. Repeat with second ball of dough.
Beat the remaining egg and the milk in a small bowl. Mix well. Brush the formed pretzels with the egg mixture and then sprinkle evenly with the poppy seeds, sesame seeds, onion flakes and kosher salt.
Bake until nicely browned, about 16 to 18 minutes. Remove from the oven and let cool. Serve warm or room temperature.