Preheat oven to 375 degrees. Line two baking sheets with parchment paper or a nonstick baking mat; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream together butter and sugar. Beat in egg, dry milk, and vanilla.
In a medium bowl, sift together flour, baking soda, and salt. With the mixer running, slowly add flour mixture to butter mixture. Fold in pecans.
Drop heaping tablespoons of batter onto prepared baking sheets about 2 inches apart. Lightly flour your fingers and press each piece of batter into a 3-inch circle.
Transfer to oven and bake until lightly browned, 8 to 10 minutes. Transfer cookies to a wire rack to cool completely.