Preheat the oven to 450°F. Spray the large rimmed baking sheet with olive oil.
In a shallow bowl, beat the eggs. In another shallow bowl, combine the breadcrumbs, Parmesan, salt, and pepper. Set half the breadcrumb mixture aside in a separate bowl.
Designate one hand as your “wet hand” (for the eggs) and one as your “dry hand” (for the breadcrumbs). Using your wet hand, drop some cauliflower pieces into the egg mixture and coat them evenly. Shake off any excess egg, then drop the coated pieces into the breadcrumb mixture. Using your dry hand, sprinkle some breadcrumbs on top and roll them around until evenly coated. Transfer the coated pieces to the prepared baking sheet and repeat with the rest of the cauliflower (when you run out of breadcrumbs, use the second bowl—this keeps the crumbs from getting too soggy).
Spray the top of the cauliflower pieces with a light coating of oil. Bake until the pieces can easily be pierced with a fork, about 20 minutes, flipping the pieces over halfway through. Serve warm.