In a medium mixing bowl, whisk together the eggs, milk, melted butter, and vanilla. Set aside.
In a large mixing bowl, combine the flour, brown sugar, baking powder, salt, and cinnamon. Pour the wet ingredients into the dry ingredients and mix until just combined.
Add the chopped bananas to the bowl and mix to combine.
Place a large pot over medium-high heat. Add 2-inches of vegetable oil to the bottom of the pot and heat until the oil reaches 350 degrees F.
Use a small cookie scoop or tablespoon to portion 3-4 scoops of the fritter dough into the hot oil. Cook for 4-5 minutes, flipping often until golden brown.
Remove the fritters from the oil and place them onto a paper towel-lined tray to drain. Repeat with the remaining dough.
Once the fritters have cooled make the glaze whisk whisking together the powdered sugar, milk, vanilla, and cinnamon in a medium mixing bowl. Dip the fritters into the glaze and then place on a wire rack over a baking sheet to let any excess glaze run off.