Heat 1 teaspoon oil in a medium pan over medium heat. Add garlic and cook until tender, but not browned, about 1 minute. Add spinach and cook, stirring, until wilted and bright green, about 1 minute.
Remove spinach from pan using a slotted spoon and let cool slightly. Squeeze out excess moisture from spinach, then pulse with basil, hazelnuts, Pecorino, and 2 tablespoons oil in a food processor until combined. Season with salt and pepper.