Preheat oven to 100º F and then turn off. This is where you will proof your dough later.
Place the yeast in the bowl of your mixer. Pour the warm water and maple syrup over top of the yeast and let sit for about 10 minutes, or until the yeast looks puffy.
While the yeast is proofing, pour the aquafaba in a separate small bowl. Whisk with a small hand whisk until it is foamy (but you are not going for the whipped meringue like foam, just a lot of bubbles).
Once the yeast has proofed, add the foamy aquafaba, salt and olive oil. Using the dough hook attachment, turn the mixer on and give it a few spins before starting to add the flour. Add the flour 1/2 cup at a time and continue kneading until the flour is all incorporated and the dough is soft and smooth. It will be soft and slightly sticky. If you press your finger in the dough it will hold the indentation of your finger for a few seconds but it will puff back out. Depending on the humidity in your kitchen it will take more or less flour.
Remove the bowl of your mixer from the mixer itself and drizzle olive oil over the dough. Turn the ball around a few times to coat with oil so it won't stick. Cover with plastic wrap or a dishtowel and place in a warm spot for the dough to rise for an hour (I like using my oven, see step 1).
After the dough has risen and doubled in size, turn it out onto a clean work surface dusted with flour. (At this point you can divide the dough and save some for later, see notes). Divide the dough into small balls to shape your rolls. I divided my dough in half, then in half again, in half one more time, and then into thirds. You want balls of dough about the size of golf balls, give or take. The full batch will make 36 balls of dough.
Work the dough slightly in your hands, stretching the top of the ball smooth and tucking the edges underneath.
Place the balls smooth side up in a baking dish (it's not a bad idea to lightly grease it first, but it's not totally necessary either!). You can use a square dish or round, you could use a large jelly roll pan, a pie plate. Just about anything that is oven safe. I have used metal pans and ceramic baking dishes and both are great.
Space the balls so that they have room to rise a second time and spread. Cover again with plastic wrap and leave in a warm area to rise for another hour. This time you can let them rise on the counter and they should be fine.
Once the rolls have risen and are now touching, preheat your oven to 350°. Brush your rolls with maple syrup, coating the tops of each roll.
Bake your rolls for 25 minutes, or until the tops are golden brown and sound slightly hollow when you tap on the tops. Remove from oven, allow to cool slightly, and serve!