In a large bowl or bread machine pan, combine flours, yeast, brown sugar, egg and water. Mix ingredients together and knead until you have achieved a soft but not sticky dough.(If using bread machine, use Dough Cycle, then turn machine off. )
Cover the dough (or shut the lid on bread machine) and allow it to rest for 30 minutes.
Preheat oven to 400˚F. Lightly grease two 9-inch pie plates or baking pans.
Divide dough into 30-35 equal-sized pieces. Take a piece of dough and place 1-2 pieces of pepperoni on top and two cubes of cheese. Wrap the dough around the pepperoni and cheese and pinch closed. Place the ball seam-side down in prepared baking dish. Repeat with the remaining dough pieces.
Before baking, brush tops pizza bites with olive oil and sprinkle evenly with Italian seasoning, Parmesan cheese and a dash of coarse salt. Bake for about 20 minutes, or until the tops are golden brown. Serve them warm with pizza or marinara sauce on the side for dipping.
Makes 30-35 bites
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