Sift the flour into a large bowl.
Add the baking powder, salt, cinnamon and nutmeg. Stir to mix.
In a medium bowl, mash the bananas until well mashed.
Add lime zest, rum and vanilla and mix.
Add butter and sugar.
Warm the evaporated milk for 30 seconds in the microwave.
Add milk and mix well for 2 minutes.
Add beaten egg and mix well for 2-3 minutes.
Add the banana mixture to the flour and mix well until thoroughly combined.
In a deep pot, heat enough oil for deep frying.
Drop 1 tablespoon for each beignet into the hot oil and fry until golden brown.
Using a slotted spoon or spider, remove the donuts from the oil.
Drain on paper towels.
To serve, sprinkle with a little powdered sugar.