Place an oven rack in the center of the oven. Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper. Set aside.
In a stand mixer, fitted with a paddle attachment, beat the butter and goat cheese together until smooth. Beat in the sugar and eggs. In batches, add the flour mixture and beat until just combined. Transfer the dough to the prepared baking sheet. With damp hands, form the dough into a 13-inch-long, 3 1/2-inch-wide loaf. Bake until light golden, about 30 minutes. Cool on the baking sheet for 30 minutes.
Transfer the loaf to a cutting board. Using a serrated knife, cut the log on the diagonal into 1/2-inch thick slices. Arrange the biscotti, cut side down, on the baking sheet. Bake until pale golden, about 15 minutes. Transfer the biscotti to a wire rack and cool completely, about 30 minutes.