In a large mixing bowl, combine 4 cups of all-purpose flour, ½ cup of granulated sugar, 2 teaspoons of active dry yeast, and 1 teaspoon of salt. In a separate bowl, whisk together 3 large eggs and 1 cup of whole milk. Pour the wet ingredients into the dry mixture, then mix until a soft dough forms. Knead the dough on a floured surface for about 10 minutes until smooth. Let it rise in a warm place for 1-2 hours, or until doubled in size.

While the dough rises, prepare your desired fills for the Thanksgiving doughnuts. For the pumpkin cheesecake filling, mix 1 cup of pumpkin puree, 8 ounces of softened cream cheese, and ½ cup of granulated sugar until smooth. For the chocolate pudding filling, follow your preferred recipe or use a store-bought version. Refrigerate both fillings for about 30 minutes until thickened, ready for assembly.

Once the brioche dough has risen, punch it down gently to remove air. Turn it out onto a floured surface and roll it to a thickness of about ½ inch. Use a round cutter to make circles. For filled doughnuts, cut an additional smaller circle in the center of half the rounds. Arrange the dough circles on a baking sheet lined with parchment paper and let them rise for another 30 minutes.

Heat oil in a deep fryer or heavy saucepan to 350°F (175°C). Carefully drop in the doughnut shapes, frying them in batches to avoid overcrowding. Cook for about 2-3 minutes on each side until they turn golden brown. Use a thermometer to check that the internal temperature reaches 190°F (90°C). Once cooked, remove them from the oil and let them drain on paper towels.

While the doughnuts are still warm, toss them in a bowl of cinnamon sugar or dip them in your prepared glaze for a sweet finish. For the glaze, mix 1 cup of powdered sugar with 2 tablespoons of reduced apple cider until smooth. Immediately coat the warm doughnuts to allow the glaze to stick, then place them on a wire rack to set slightly before serving.