The batter is very runny, but don't worry about this, because that's what makes these cookies as light as they are; they literally melt in your mouth. If you want a stiffer, heavier cookie, add 1/4 cup whole-wheat flour or unbleached white flour to the recipe, and delete 1 teaspoon baking powder. These cookies are very soft and cakelike.

Preheat the oven to 350 degrees F. Cream together the oil and honey. Beat in the eggs, vanilla, and peanut butter, then stir in the mashed banana. Sift together the flour, baking powder, and salt and stir into the liquid mixture. Blend well. Drop onto oiled baking sheets by scant tablespoonfuls 1 inch apart and bake for 12 to 15 minutes. Cool on racks.