In the bowl of a stand mixer, stir together 2 cups of the all-purpose flour, sugar, yeast and table salt. With the mixer on low, pour in the butter-beer mixture, mixing just until the flour is moistened. Add eggs, one at a time, and mix until combined. Add the remaining 1/2 cup all-purpose flour and all of the rye flour, mixing just until combined. Replace paddle with a dough hook and knead the dough for 3 to 4 minutes on low.