Cut browned butter into squares; loosen squares from baking dish, and let stand at room temperature until very soft, 1 to 1½ hours.
Assemble Ankarsrum mixer with plastic bowl and balloon whisks. Add butter and salt. Beat at high speed (6 o’clock) until creamed together, about 1 minute, stopping halfway to scrape sides of bowl. With mixer on lowest speed (12 o’clock), gradually add confectioners’ sugar alternately with milk, beginning and ending with confectioners’ sugar, beating until combined after each addition. Add vanilla. Gradually increase mixer speed to medium-high (5 o’clock), and beat until fluffy, about 2 minutes. Stir in pecans. Use immediately.
Recipe by Bake from Scratch at https://bakefromscratch.com/browned-butter-pecan-cake/