In a small bowl, whisk together the active dry yeast and granulated sugar into the warm milk, and let it stand for 5 to 10 minutes until it becomes frothy.

In a large mixing bowl, combine the all-purpose flour, salt, and ground cinnamon, whisking gently to distribute the spices evenly.

Pour the frothy yeast mixture and the beaten egg into the dry ingredients, then stir vigorously with a wooden spoon until a smooth, very sticky batter forms.

Gently fold the finely diced apple and raisins into the batter until they are evenly distributed throughout the mixture.

Cover the bowl with a damp kitchen towel and let the batter rise in a warm, draft-free place for about 1 hour, or until it has doubled in size and looks bubbly.

Heat the vegetable oil in a heavy-bottomed Dutch oven over medium heat until it reaches 375°F (190°C) on a deep-fry thermometer.

Using two metal spoons or a greased ice cream scoop, carefully drop round mounds of batter into the hot oil, cooking only 4 to 5 at a time to avoid crowding the pot.

Fry the doughnuts for 5 to 6 minutes, gently turning them over halfway through, until they are deep golden brown and cooked through to the center.

Use a slotted spoon to transfer the fried doughnuts to a wire rack lined with paper towels to drain any excess oil.

Dust the warm Dutch doughnuts generously with powdered sugar and serve them immediately while they are still hot and crispy.