Preheat the oven to 400°F. Line a baking sheet with parchment paper, lightly grease with olive oil, and set aside.
In a food processor, combine the carrot, chickpeas, onion, garlic, and 2 tablespoons olive oil, and blend until finely chopped, but not too smooth, about 30-60 seconds. Transfer the mixture to a large bowl, season with salt, black pepper, and red pepper flakes. Add the oat flour and stir everything together until well combined.
Scoop out 1 tablespoon of the mixture at a time and roll it into a ball in your hands. Repeat with the rest of the mixture; you should end up with 15 balls. Place the veggie balls on the prepared baking sheet and brush them with the remaining olive oil. Bake for 35 minutes, flipping halfway through. Remove from the oven once both sides are browned.
Allow to cool for a few minutes, then poke with toothpicks, add an olive to each ball, and transfer them to a plate.