Use a knife to perforate the acorn squash with several slits. Cook in microwave for 10 minutes. Scrape the flesh into a bowl. Stir in the garlic, 1/2 teaspoon salt, egg, and whole wheat flour. Add the white flour in small amounts and mix until you get a sticky dough with a manageable texture. Turn the dough out onto a floured surface and roll into thin ropes. Slice the dough into quarter-sized gnocchi.
Bring the water with 1 tablespoon salt to a boil in a large pot; add the gnocchi to the boiling water one at a time, until they are all floating at the top; remove with a slotted spoon to a large bowl; set aside.
Discard all but 1 1/2 cups of the water from the pot and return to heat; add the bouillon cube, beer, sage, and pepper and bring to a boil; continue to boil until the mixture reduces to about half its original volume, about 15 minutes; reduce heat to medium. Whisk the butter cubes into the mixture, one at a time, until they are all melted into the liquid; immediately return the gnocchi to the mixture, turn off the heat, and stir in the Parmesan cheese. Cover the pot and allow to sit for 10 minutes before serving.
