Combine flour, salt, sugar, and yeast in the bowl of a stand mixer, making sure the salt and yeast aren't touching. Pour the tomato sauce into the center of the bowl along with the oregano and garlic powder. Mix on low speed until the dough comes together on the dough hook, pausing occasionally to push dry ingredients into the center.
If there are still quite a lot of dry ingredients in the bottom of the bowl after about 5 minutes, add up to 1½ tablespoon warm water 1 teaspoon at a time, sprinkling it onto the dry spots in the bowl and letting the mixer run for at least 30-60 seconds before deciding if you need to add more water.Resist adding water unless absolutely necessary. The dough will hydrate more fully as it rests. It's better to have a slightly dry bagel dough than a dough that's too wet.
Add the thinly sliced fresh basil and increase speed to medium. Knead 3 minutes until dough is smooth, tacky, and slightly stretchy.
Tuck the ends under the dough to shape it into a ball, then place in a lightly oiled bowl, cover, and let rise for 1 hour in a warm spot. It should just about double in size and when you press a finger into it, the indentation should spring back slightly.
Gently deflate the dough, knocking the air bubbles out of it. Cover and let rest 10 minutes.
Preheat your oven to 425°F and bring a wide, deep pan or large pot filled with at least 3 inches of water to a low boil on the stove.
Divide the dough into 8 equal pieces with a kitchen scale. Shape them into balls by gently flattening each piece against a clean, un-floured countertop, folding the edges into the center and pinching them together to form a smooth surface on the underside of the dough.Flip the dough over so the smooth side is on top. Cup your hand around the dough ball in a claw shape with your pinkie against the counter, and drag your hand towards your body. Rotate the dough 90 degrees and repeat as needed until you have a smooth ball with a seam on the bottom.
Dust your hands with in flour and poke a thumb through the seam-side of each dough ball, pushing any stray edges into the middle. Slide your other thumb in and gently rotate the bagel ring through your hands, stretching the dough until the hole in the middle is twice as wide as the sides of the bagel.
Arrange the bagels on a silicone or parchment lined sheet pan. Cover with a damp paper towel and let them rest for 10 minutes.
While the bagels rest, use a large (3") and a small (1") round cutter to cut 8 mozzarella slices into bagel shapes.
Immediately before boiling, stretch the bagels again so the holes are twice as wide as the sides. Then slide them into the pot of boiling water, top-side down. Work in batches of 2-4, depending on how big your pot is.
Boil bagels for 1 minute per side, then use a wire spider to return them to the baking sheet.
Brush bagels with egg wash, then top each pizza bagel with 4 pepperoni slices, a ring of thinly sliced mozzarella cheese, and a dusting of parmesan cheese.
Bake for 20 minutes at 425°F.
Remove the bagels from the oven and transfer immediately to a wire rack to cool completely.
To test if your dough is ready after it rests for an hour, gently press into it with one finger. If it immediately fills in the indentation when you remove your finger, your dough needs more time to rise. If the indentation only fills in part way or fills in very slowly, your dough is ready. If it doesn’t fill in at all or the dough seems to collapse, your dough has overproofed.
You can mix in a ¼ cup of your preferred topping right into the dough to infuse your bagels with maximum flavor. Just make sure your topping doesn’t include salt, or it can throw off the chemistry of the dough.
Store in an airtight bag with a paper towel to absorb moisture. Stored properly, they will stay good for 3-4 days. They’ll get a bit hard after the first day or so, but soften up if you toast them. You can also run them briefly under water (!!!), then microwave them for 10 seconds, slice them, and toast them (or put them on a rack in your regular oven for 10 minutes at 350°F).