Place the green beans in a microwave-safe bowl. Cover and steam until soft, about 4 minutes.
Heat the oil in a large sauté pan over medium heat. Cook garlic until fragrant but not browned, about 1 minute. Remove from heat and add beans to saucepan, tossing to coat with oil and garlic.
Transfer beans to a food processor or blender. Add basil and puree, thinning with water or additional olive oil, to desired consistency for baby.