Preheat oven to 350°F. Lightly grease two standard donut pans.
In a small bowl, stir together the ground flax and water. Set aside to thicken for 5 minutes.
In a large mixing bowl, mash the ripe bananas. Mix in the flour, sugar, melted butter, vanilla, baking powder, baking soda, cinnamon, nutmeg, and salt. Finally, stir in the flax mixture, being careful not to overmix.
Fill the greased donut pans 3/4 of the way full with batter (use a piping bag for less mess). Bake for 10 minutes, then transfer donuts to a wire rack to cool.
For the Maple Glaze
In a medium microwave-safe bowl, melt the vegan butter. Whisk in the maple syrup, powdered sugar, cinnamon, and vanilla until smooth.
Dip the top of each donut in the glaze, then return to rack with glaze-side-up to set. Repeat 1 or 2 more times for a thicker coating of glaze.