1. Preheat the oven to 250°. With a pastry brush, spread the softened butter evenly over two large baking sheets and set them aside.
2. With a wire whisk or a rotary or electric beater, beat the egg white until it is stiff enough to form soft peaks on the whisk or beater when it is lifted from the bowl.
3. Beat in the brown sugar about ¼ cup at a time, and continue to beat until the meringue mixture is very stiff and no longer glossy. With a rubber spatula, gently fold in the pecan halves.
4. To form each pecan drop, scoop up 1 tablespoonful of the meringue mixture and, with the aid of another spoon, slide it in a small mound onto the buttered baking sheets.
5. Arrange the pecan drops about 1 inch apart to allow them to spread slightly. Bake in the middle of the oven for about 30 minutes, or until the pecan drops have lost all their sheen and are a pale biscuit color. With a spatula, transfer them to a cake rack to cool before serving.
