Stir in the flour, using extra flour or water as needed to make a soft dough that isn't too sticky.
Turn out onto a floured board and knead for a couple of minutes. Shape into a ball and let raise in a bowl for 30 minutes to an hour, covered with a towel. Volume should double.
Turn the raised dough back onto the floured board, and cut it into 12 pieces (I use a scraper/cutter, but a knife works fine.).
Take each piece, flatten it lightly on the board with your hand, and place 4-5 slices of pepperoni in the middle, overlapping but not stacked.
Roll it up like a jelly roll, and then crimp it with your fingers to seal the ends into an oval, with no pepperoni sticking out. Place on an ungreased baking sheet with at least an inch between each one.
Beat in an egg and add a tablespoonful of water. Brush rolls lightly with this glaze. You don't need to let the rolls raise further, but you can if you want to.