In a large bowl, whisk together the flour, granulated sugar, baking powder, salt, cinnamon, and nutmeg until well combined.
In a separate bowl, mix the milk, melted butter, egg, vanilla extract, and cooled chai tea until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Heat oil in a deep fryer or large pot to 350°F (175°C).
Using a spoon or a piping bag, drop spoonfuls of the doughnut batter into the hot oil, frying a few at a time until golden brown, about 2-3 minutes per side.
Remove the doughnuts from the oil and drain on paper towels. Allow them to cool slightly.
In a medium bowl, whip the heavy cream with the powdered sugar and vanilla extract until stiff peaks form.
Once the doughnuts are cool, use a piping bag to fill each doughnut with the whipped cream.
Dust the filled doughnuts with powdered sugar before serving.