Add the chopped veggies to a skillet or a large pot with some water and cook over medium-high heat for 5 minutes. Add more water if needed. Feel free to sauté the veggies in some oil if you want, but omit the tahini.
Add the chopped tomatoes and cook another 5 minutes.
Add the tamari or soy sauce and the spices and stir. Then add the rice and the water or broth and bring to a boil. Cook over medium-high heat for 15 minutes or until the rice is cooked.
Add the tahini (optional), chickpeas and beans, stir and cook 1 to 2 minutes more.
Serve with some chopped fresh parsley on top (optional).
Keep the vegan jambalaya in the fridge in a sealed container for 4 to 5 days.