Mix together ground flaxseed and water. Set aside.
Bring a pan to medium-high heat on the stovetop and add the pepper, onion, and just a bit of water to prevent sticking. Sauté for 3-5 minutes, until the onion just starts to become translucent. Add the garlic and sauté another 1-2 minutes. Remove from heat and set off to the side.
Reserve ¼ cup of the black beans and set to the side. Mash the remaining black beans with a fork or a potato masher until they make a paste. (I like to leave some chunks, but you can make this as smooth or chunky as you'd like - just as long as it sticks together like a thick paste.)
Add the sautéed veggies, the ¼ cup of reserved beans, ketchup, tamari, and all spices to the mashed beans. Mix to combine.
Add the flour and the flax egg (which should have thickened by now and become an egg-like consistency). Mix to combine.
Form into 3 patties, using about ½ cup for each patty.
Place patties on parchment paper on a plate or small baking sheet and refrigerate for 30 minutes to slightly firm up.
Bring a nonstick pan on the stove top to medium heat and cook your patties to your liking, usually 1-3 minutes on each side.
Assemble your burgers with whatever toppings you'd like!