Heat oven to 375.
Bring a large pot of water with the chopped potatoes to a boil. Cook until fork tender.
While the potatoes are boiling, heat the oil in a large pot over medium heat.
Add the carrots and bay leaf, sauteing until the carrots have softened, about 5 minutes.
Add the broccoli, cauliflower, peas, chickpeas, tamari, thyme, and black pepper and salt to taste.
Cook until the frozen veggies are just heated through, then remove the bay leaf.
Transfer the vegetable mixture to a greased glass 8x8 baking dish.
Once the potatoes are tender, drain and run the potatoes through a potato ricer. If you do not have a potato ricer, carefully peal the cooked potatoes and lightly mash with a fork.
Fold the butter into the potatoes. Then slowly add the warmed milk and broth, until your desired texture is reached. I didn't use all of the liquid.
Gently fold in the nutritional yeast, cayenne pepper, black pepper, and salt.
Smooth the mashed potatoes over the veggies, then sprinkle with vegan Parmesan, if you wish.
Bake for 30 minutes, or until hot and the potatoes are lightly golden brown along the edges.