Preheat oven to 400°F. Lightly grease a baking sheet with olive oil. Set three bowls next to the baking sheet. Add flour to the first bowl and eggs to the second. Beat the eggs lightly with a whisk or fork.
In the last bowl, combine the panko, Parmesan, salt, garlic, paprika, and pepper. Stir together and drizzle with olive oil, stirring again to mix throughout and form larger crumbs.
Add a handful of Brussels sprouts to the flour and toss to coat. Transfer them to the egg mixture. Dunk them in the eggs and roll them through the panko mixture in the last bowl.
When the Brussels are well coated, place them on the greased baking sheet. Bake until golden brown with crispy edges, about 20-22 minutes. Remove from the oven and serve warm.