Make the pizza dough. Combine active dry yeast with sugar and warm water in a small bowl. Let the mixture sit for 5 minutes or until it becomes foamy and the yeast is activated.
Combine all-purpose flour with oil and salt in a large bowl. Add the yeast mixture and mix until a dough forms. Knead for 5-7 minutes or until the dough is smooth. Cover and proof in a warm area until doubled in size, about 1 hour.
Punch down the dough. Portion the dough into 20 equal balls, about 30 grams each. Arrange the rolled-out dough in a 10-inch cake pan or springform pan, leaving space around each portion.
Combine the melted butter with everything bagel spice, garlic powder, and pepper. Drizzle the seasoned butter over the dough, making sure to coat all sides of the dough. Sprinkle the grated parmesan and mozzarella on top and around the sides of the dough balls. Cover and let rise for 30 minutes in a warm area.
Preheat oven to 375 degrees F.
If you are using a springform pan, place the pan on a baking sheet. Bake the everything bagel cheesy monkey bread for 25-30 minutes or until the bread is nicely browned. Serve warm.
Notes
If you can't find everything bagel spice, you can make it yourself. Combine 2 teaspoons white sesame seeds with 1 ½ teaspoons dried minced onion, 1 ½ teaspoons dried minced garlic, 1 ½ teaspoons black sesame sesame seeds, 1 teaspoon sea salt flakes, and ½ teaspoon poppy seeds. Reserve the extra seasoning for another use.