In a large mixing bowl, whisk together 2 cups of all-purpose flour, ½ cup of granulated sugar, 1 tablespoon of baking powder, ½ teaspoon of salt, ½ teaspoon of ground cinnamon, and ¼ teaspoon of ground nutmeg until well combined.

In another bowl, combine ½ cup of milk, 2 large eggs, 1 teaspoon of vanilla extract, and ¼ cup of melted butter. Whisk these ingredients together until smooth and creamy. Pour the wet mixture into the bowl of dry ingredients, gently stirring until just combined.

Fill a deep fryer or a heavy pot with oil suitable for frying and heat it to 350°F (175°C).

Carefully drop spoonfuls of batter into the hot oil, frying the donuts for about 2-3 minutes on each side until they turn a rich golden brown.

In a medium saucepan over medium heat, warm 1 cup of heavy cream with 1 teaspoon of vanilla extract until just steaming. In a separate bowl, whisk together 4 egg yolks and ¼ cup of brown sugar until smooth. Gradually pour the warm cream into the egg mixture while whisking continuously.

Return the custard mixture to the saucepan and cook over low heat, stirring constantly until it thickens slightly, about 5-7 minutes.

Using a piping bag, carefully fill each cooled donut with the custard until plump and full.

Sprinkle a layer of granulated sugar over the top of each filled donut. Using a kitchen torch, carefully melt the sugar until it forms a crispy caramelized crust.

Allow the caramel to set for a moment, then arrange your donuts on a serving platter. Enjoy warm or at room temperature.