Add the diced carrots, celery, bell pepper, and potatoes to the pot. Cook, stirring occasionally, for about 5 minutes or until the vegetables start to soften.
Stir in the chopped tomatoes, dried thyme, dried rosemary, paprika, salt, and pepper. Cook for another 2 minutes, allowing the flavors to meld together.
Pour in the vegetable broth, and bring the stew to a simmer. Reduce the heat to low, cover the pot, and let it simmer for 20-25 minutes or until the vegetables are tender.
Once the vegetables are cooked through, stir in the chopped kale or spinach. Let it cook for an additional 3-4 minutes until the greens are wilted and tender.
Taste the stew and adjust the seasoning if needed. You can add more salt, pepper, or herbs according to your taste preference.
Serve the vegan veggie stew hot, garnished with fresh parsley if desired. Enjoy with crusty bread or over a bed of cooked grains like rice or quinoa.