Beat butter in a stand mixer fitted with a paddle attachment on medium speed until creamy, about 1 minute. Gradually add powdered sugar, beating until mixture is smooth, about 1 minute. Stir in chopped toasted pecans and vanilla.

Whisk together flour and baking powder in a bowl. With mixer running on low speed, gradually add flour mixture to butter mixture until blended.

Transfer dough to a work surface; shape into 2 (7-inch) logs. Wrap logs separately in plastic wrap; refrigerate at least 4 hours or up to 2 days.

Preheat oven to 350°F. Line 2 baking sheets with parchment paper. Place turbinado sugar in a shallow dish. Unwrap logs, and brush evenly on all sides with egg. Roll each log in turbinado sugar. Cut logs into 1/3-inch-thick slices (you should have 42 cookies total), and place 1 inch apart on prepared baking sheets. Top each cookie with 1 pecan half, pressing lightly to adhere.

Bake in preheated oven until cookie edges are golden, 10 to 12 minutes. Let cool 5 minutes on baking sheets. Transfer cookies to a wire rack; cool 10 minutes.