In the bowl of an electric mixer, combine the brown sugar, salt, vanilla and pecan pieces. Beat on low speed to incorporate the ingredients, then drizzle in the egg whites. Increase the speed to medium-low and beat for 4 to 5 minutes, scraping down the sides of the bowl as needed.
Drop the dough in rounded tablespoons onto a greased baking sheet. Press each ball of dough with the back of a spoon to form a cookie 3 1/2 inches in diameter and about 1/4 inch thick.
Bake 10 to 12 minutes, until the edges are lightly browned. Remove from oven and cool for 3-5 minutes on the baking sheet, then use a thin spatula coated with pan spray to remove the cookies to a cooling rack. The cookies will be soft but will firm up as they cool.
Keep in a sealed container at room temperature for 3-4 days.