Put butter and granulated sugar into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until pale and fluffy, 2 to 3 minutes. Mix in vanilla. Reduce speed to low, and gradually mix in flour, salt, and pecans. Wrap in plastic, and refrigerate until firm, about 1 hour.
Preheat oven to 325. Shape dough into 1 1/4-inch balls, and space 2 inches apart on parchment-lined baking sheets. Press thumb into center of each cookie. Bake 10 minutes. Remove from oven; press centers with the end of a wooden spoon. Bake until golden brown, 10 to 15 minutes. Let cool completely on sheets.
Stir together confectioners' sugar and milk; tint pink. Fill centers with icing. Let set overnight. Cookies can be stored in airtight containers up to 1 week.
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