Preheat oven to 325°F. Arrange black beans on a baking sheet lined with parchment paper and bake for 10-15 minutes. The beans should be slightly dried out and not wet.
Mix together ground flax and water and set aside to gel.
Meanwhile, cook onion, celery, and garlic in oil or water in a pan over medium heat for about 5 minutes, or until onion turns translucent. Remove from heat and let cool as you prepare the next step.
Once the beans have dried out slightly, take out of the oven and briefly cool. Place in a mixing bowl and mash beans with a fork, leaving about half the beans whole.
Once you've mashed the beans, add in the cooked veggies and remaining ingredients. Mix until combined. Let sit for a few minutes as you heat up the waffle iron.
Lightly oil both sides of your waffle iron so the black bean mixture does not stick. When your waffle iron is heated, add a big spoonful of the mixture into each section of your waffle iron (as opposed to one spoonful in the center, as this mixture will not spread like a typical waffle batter). Close your waffle iron and let your waffles cook. They will be firm and browned on the outsides when they are ready (about 3 minutes, depending on your waffle maker).