Preheat the oven to 350F.
In a 5-quart Dutch oven, or cast-iron pot, heat avocado oil over medium-high heat.
Pat lamb shanks dry with a paper towel, season with salt and pepper, and sear on each side until you begin to see color in the lamb and in the pot.
Remove the shanks from the pot and set aside.
Reduce heat to medium low. Add onions, carrots, and garlic cloves. Cook until the onions are translucent.
Add vinegar to the pot, scraping the bottom to deglaze the pan.
Add tomato paste and starch, and stir thoroughly.
Add wine and stir until heavy and thick.
Add the broth and the herbs to the pot and stir to combine. Sauce should barely coat a spoon but not stick.
Return the shanks to the pot, arranging to ensure they are fully submerged in liquid.
Cover pot with lid and cook in the oven for 2.5 hours.
Remove the pot from the oven and add in eggplant, zucchini, red pepper and olives. Return to the oven for 30 minutes.
Remove bay leaf and rosemary and serve.