Preheat oven to 425 degrees F (220 degrees C). Grease a 10x15-inch baking pan with cooking spray.
Arrange potato wedges in a single layer on the prepared pan.
Combine basil, nutritional yeast, almonds, and garlic in a blender or food processor. Blend, gradually pouring in 2 tablespoons plus 2 teaspoons olive oil, until pesto is smooth. Season with salt and pepper. Coat potatoes with the pesto.
Bake in the preheated oven, turning once halfway, until crispy and golden, about 45 minutes.