In a large bowl, mash bananas with a fork (or hands), then add flour (a little less than one part flour to one part banana). Continue to mix until mixture resembles thick pancake batter, adding more flour if needed. Mix in baking powder and salt.
Using an ice cream scoop, add balls of banana mixture to the hot oil. Fry until golden brown, flipping over for even browning. Using the mesh strainer, remove from the oil, and drain on paper towels.