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 cinnamon, and ¼ teaspoon of nutmeg until well combined.

In a separate bowl, mix together ½ cup of milk, 2 large eggs, 1 teaspoon of vanilla extract, and ¼ cup of melted butter until smooth.

Heat oil in a deep fryer or large heavy pot to 350°F (175°C). Fry the donuts for about 2-3 minutes on each side until golden brown.

In a medium saucepan, combine 1 cup of heavy cream and 1 teaspoon of vanilla extract. In a separate bowl, whisk together 6 egg yolks and ¼ cup of brown sugar until smooth.

Pour the custard mixture back into the saucepan and cook over low heat until thickened (about 8-10 minutes).

Fill a piping bag with the cooled custard and fill each donut generously.

Spread granulated sugar on a heatproof surface, and using a kitchen torch, melt the sugar until it forms a crispy, golden crust.

Serve the Caramelized Crème Brûlée Donuts warm or at room temperature.