In a large skillet or pot, heat cooking oil over medium heat. Saute onion for 2-3 minutes, stir in garlic and cook for 2-3 minutes more. Stir regularly.
Add bell pepper and eggplant. Cook for 5 minutes. Stir regularly.
Stir in tomatoes, sweet potatoes, water, balsamic vinegar, rosemary, bay leaf, salt, and pepper. Stir well. Reduce heat to simmer, cover, and cook for 20-30 minutes. Add more water during cooking if needed. Stir regularly.
To make the chia egg, combine chia seeds and water (1 egg = 1 tbsp chia seeds + 3 tbsp water). Mix well and let sit for a few minutes.
Combine all burger ingredients in a small blender or food processor. Do not over process, you want to keep some texture in it. Add a little water if too dry or more panko if too wet
Make into burger patties. Heat cooking oil over medium heat and cook burger patties on both sides until cooked through and golden.
Serve with Provencal stew.