Add oil and flour to a pan and cook over med-high heat, whisking constantly, until it turns a dark caramel color (makes a roux sauce). May take up to 10 minutes. Pour into crockpot (or pot, if cooking on stove). Let cool a little bit, then add tomatoes and stir to combine. Turn heat to medium in crockpot or medium low on stove.
Cook sausage and chicken, if using, in same pan as the roux; add oil if needed to prevent sticking. Set aside when done.
Add all vegetables (pepper through okra) to tomato/roux mixture in pot or crockpot; stir after each addition. Add vegetable broth as needed; it should be more stew-like than soup-like, but all the veggies should be covered with liquid so that they cook evenly.
Strip the leaves off half of the thyme sprigs and add to gumbo. Add remaining sprigs and bay leaves directly to gumbo (remove before serving). Add cumin, salt, pepper, and chili powder (just a little!) to taste. Stir when you think about it. :-)
Let cook until carrots start to become tender (1-2 hrs?). 1/2 hour before serving, stir in vegan sausage/chicken. Let continue cooking until serving.
This with cornbread on the side is pretty good!
p.s. any veggies can work...turnips, rutabagas, corn, peas, etc.