In the bowl of a stand mixer fitted with the paddle attachment, beat butter and brown sugar at medium speed until fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Beat in vanilla bean paste.
In a small bowl, whisk together flour and salt. Add flour mixture to butter mixture all at once; beat at low speed just until combined. Fold in chocolate. Cover and set aside until ready to use.
In a medium bowl, stir together all ingredients until smooth. Use immediately.
Recipe by Bake from Scratch at https://bakefromscratch.com/cookies-milk-bundt-cake/