In a large mixing bowl, combine your brioche dough ingredients: flour, granulated sugar, eggs, and heavy cream. Mix until a shaggy dough forms, then knead on a floured surface for about 10 minutes until smooth and elastic. Allow the dough to rise in a greased bowl, covered with a damp cloth, in a warm area for 1-2 hours, or until it has doubled in size.

Once risen, punch down the dough to release air. Roll it out on a floured surface to about ½ inch thickness. Cut dough into desired shapes using a doughnut cutter or round cups. Place the cut doughnuts on a parchment-lined baking sheet, and let them rise again for 30 minutes or until slightly puffy.

Meanwhile, heat oil in a deep pot or frying pan to 350°F (175°C). Carefully drop the risen doughnuts into the hot oil, frying them in batches to avoid overcrowding. Fry for 2-3 minutes on each side until they are golden brown and puffed up. Use a slotted spoon to remove them, allowing excess oil to drain on paper towels.

Let the fried doughnuts cool slightly before filling them with your chosen fillings, like pumpkin cheesecake or apple pie. Use a piping bag to inject the filling into the center of each doughnut. For glazed variants, dip the tops of each doughnut in your prepared glazes.

Although tempting to sample right away, allow the filled doughnuts to rest for a few minutes. These delightful treats are best enjoyed fresh.