1. Dissolve sugar and yeast in 1 cup warm water in a small bowl; let stand 5 minutes.
2. Combine oil, vinegar, and egg yolks in a small bowl, stirring with a whisk. Place mozzarella cheese and cheddar cheese in a bowl, stirring to combine. Chill.
3. Weigh or lightly spoon flours, potato starch, and flaxseed meal into dry measuring cups; level with a knife. Combine flours, potato starch, flaxseed meal, xanthan gum, and salt in the bowl of a stand mixer fitted with a paddle attachment; beat at medium speed until blended. Slowly add yeast mixture and oil mixture, beating until blended and dough pulls away from sides of bowl.
4. Turn dough onto a lightly floured surface; divide dough into 4 equal portions. Shape each portion into a ball. Working with 1 portion at a time (cover remaining portions to prevent drying), roll each portion into a 12 x 6-inch rectangle on a floured surface. Place one-fourth of pepperoni slices down center of dough leaving a 1-inch border at top and bottom; top with one-fourth cheese mixture. Beginning at short side, roll up dough tightly, jelly-roll fashion; pinch seams and ends to seal. Repeat procedure with remaining dough portions. Place rolls, seam sides down, 2 inches apart on baking sheets covered in parchment paper. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size.
5. Preheat oven to 375°.
6. Combine Parmesan cheese and oregano in a small bowl, stirring to combine. Place egg whites in a bowl, stirring well with a whisk. Brush tops of dough with egg whites; sprinkle with Parmesan cheese mixture.
7. Bake at 375° for 35 minutes or until crust is golden brown. Remove from pans; cool completely on wire racks.