Sift cake flour, salt, and baking powder into a medium bowl.
Combine butter, sugar, and vanilla extract in a large bowl; beat with an electric mixer until smooth and creamy. Add dry ingredients and mix thoroughly. Shape dough into a 1-inch diameter log, wrap with plastic wrap, and place in the refrigerator until firm, 1 hour to overnight.
Preheat the oven to 275 degrees F (135 degrees C). Line 2 cookie sheets with parchment paper.
Remove dough from the refrigerator and slice into 24 slices. Place on the prepared cookie sheets and press a pecan firmly into each slice.
Bake in the preheated oven until edges are golden, about 40 minutes. Cool on the baking sheet for 1 minute before removing to a wire rack to cool completely.