In a medium saucepan, melt butter over medium heat. Cook, swirling pan occasionally, until butter turns a medium-brown color and has a nutty aroma, about 10 minutes. Remove from heat, and let cool to room temperature. Pour browned butter into a medium bowl, being sure to include all browned bits from bottom of pan.
Refrigerate butter, stirring every 30 minutes to reincorporate browned bits, until butter holds a shape but is still pliable, about 1 hour. Transfer butter to a large a piece of plastic wrap, and shape butter into a square. Wrap butter in plastic wrap, and refrigerate until cold and solidified, about 2 hours.
Preheat oven to 375°. Line large baking sheets with parchment paper.
In a large bowl, combine flour, sage, salt, baking powder, and baking soda. Cut cold browned butter into ½-inch pieces, and add to flour mixture along with goat cheese. Using a pastry blender, cut in butter and goat cheese until mixture is crumbly. Gradually add 1¼ cups buttermilk, stirring just until dough comes together. If dough seems dry, add remaining ¼ cup buttermilk, 1 tablespoon at a time.
Turn out dough onto a lightly floured surface, and using your hands, pat dough to 1-inch thickness. Using a 3-inch round cutter, cut dough, rerolling scraps as necessary. Place on prepared pans.
Bake until golden brown, about 20 to 23 minutes.
Recipe by Bake from Scratch at https://bakefromscratch.com/browned-butter-biscuits-sage-goat-cheese/