Heat about 2 inches vegetable oil in a large skillet over medium-high heat until a deep-fry thermometer registers 375 degrees F.
Meanwhile, whisk the flour, baking powder, salt, 1/4 teaspoon cinnamon and 1/3 cup granulated sugar in a large bowl.
Whisk the egg, milk, mashed banana and 2 tablespoons vegetable oil in another bowl. Add the banana extract, if desired. Combine the remaining 1/2 cup granulated sugar and 1 teaspoon cinnamon in a shallow bowl and set aside.
Whisk the banana mixture into the dry ingredients until just moistened. Working in batches, drop rounded teaspoonfuls of dough into the hot oil and fry until golden brown, about 15 seconds per side. Remove with a slotted spoon and drain on paper towels, then roll in the cinnamon sugar while still warm.