In the bowl of a stand mixer fitted with the paddle attachment, beat butter and vanilla at medium speed until smooth, 2 to 3 minutes.
With mixer on low speed, gradually add 1¾ cups confectioners’ sugar; increase mixer speed to medium, and beat until light and creamy, stopping to scrape sides of bowl. With mixer on low speed, gradually add flour and salt, beating until combined. (Mixture will seem crumbly.) Slowly increase mixer speed to medium-high, and beat until dough comes together, about 1 minute.
Line 2 baking sheets with parchment paper.
Using a 1½-tablespoon spring-loaded scoop, scoop dough, and roll in your hands to smooth. Place 1½ inches apart on prepared pans. Cover and refrigerate until firm, at least 20 minutes, or up to overnight.
In the work bowl of a food processor, pulse freeze-dried fruit and remaining ¾ cup confectioners’ sugar until smooth and evenly colored. (See note.) Sift fruit-sugar mixture into a shallow bowl to remove any seeds and lumps of sugar.
Preheat oven to 375°.
Bake, one pan at a time, until golden and set, 10 to 13 minutes. Let cool on pans until easy to handle, about 5 minutes. Roll warm cookies in fruit-sugar mixture, and let cool completely on a wire rack. Roll cooled cookies in fruit-sugar mixture again. Store in an airtight container for up to 1 week.
Notes
Add some color to these tender cookies by using ¼ cup each blueberry, strawberry, and peach in separate batches for three colors of cookies. Sugars can be stored in an airtight container for up to 1 week.
Recipe by Louisiana Cookin' at https://louisianacookin.com/pastel-butter-cookies/