How to Make It
Place chopped toasted pecans and milk in a small bowl, and let stand at room temperature until milk is mostly absorbed, about 30 minutes.
Preheat oven to 375°F with oven racks in the top third and bottom third of oven. Beat butter and 3/4 cup of the sugar with an electric mixer on medium speed until light and fluffy, about 2 minutes. Add egg and vanilla, and beat on low speed just until combined. Add flour and chopped toasted pecans alternately to butter mixture, beginning and ending with flour. Beat on low speed just until incorporated after each addition. Drop by tablespoonfuls about 2 inches apart on parchment paper-lined baking sheets. Press 1 pecan half into top of each cookie. Brush pecans lightly with egg white, and sprinkle evenly with remaining 1 tablespoon sugar.
Bake in preheated oven until cookies are just set, about 10 minutes, switching pans top rack to bottom rack halfway through baking. Cool on pans on wire rack 5 minutes; transfer cookies to wire rack, and cool completely, about 30 minutes.