Preheat the oven to 400℉. Line a large rimmed baking sheet with parchment paper.
Place the grated zucchini in a strainer over a bowl. Sprinkle it with 1 tsp of salt and toss to coat. Let sit for 10-15 minutes to draw out the water.
While the zucchini is draining, place the chickpeas, sun dried tomatoes, and chopped basil in the food processor. Pulse until the everything is combined (there may be a few chunks of tomato that don't get fully ground up, and that's okay).
After 10-15 minutes, wrap the zucchini in a clean, dry kitchen towel or paper towels and squeeze out any remaining water, then add it to the food processor with the rest of the falafel ingredients (breadcrumbs, garlic, and seasonings).
Pulse the mixture a few times until everything is combined. If you mixture seems too moist, add some additional breadcrumbs.
Roll the mixture into small balls (mine were about the size of a golf ball). Place them onto the prepared pan. Bake for 20 minutes. Flip them and bake 20 minutes more. While they bake, make the balsamic glaze!