Mix goat cheese, honey, and basil together in a bowl until smooth and creamy; refrigerate for 20 minutes.
Preheat toaster oven or oven to 400 degrees F (200 degrees C).
Fill dates with goat cheese filling using a small spoon. Wrap each date with enough prosciutto to cover entire date and secure with a toothpick. Arrange on a baking sheet.
Bake in the preheated toaster oven until prosciutto becomes crisp and caramelized, about 10 minutes. Flip each date and continue baking until crisp on top, about 5 more minutes.
