Preheat the oven to 425 degrees F (220 degrees C). Place pizza on a baking sheet.
Bake in the preheated oven for 13 to 15 minutes.
Meanwhile, heat olive oil in a frying pan. Saute bacon, onion, and bell pepper in the hot oil until tender, 8 to 10 minutes. Drain off any grease and return to the pan. Add chopped spinach and garlic; stir until spinach is wilted. Remove from the pan to a small bowl to let cool for a few minutes.
Remove pizza from oven. Leave oven on. Add egg whites to vegetable mixture; stir to combine.
Carefully top pizza with vegetable-egg mixture. Pour slowly so eggs don't run off the sides. Use a spoon to catch any drips and return to the top of the pizza.
Bake in the preheated oven for 10 minutes. Top with Cheddar cheese and bake for 5 minutes more. Remove from the oven and top with fresh basil.