Preheat the oven to 350°F and grease an 8” x 18” casserole dish with cooking spray.
Fill a medium-large pot halfway with water and bring to a boil. Add green beans and carrots, boiling for 3 minutes.
Add frozen corn and boil for 2 more minutes.
Drain cooked veggies and set aside in the strainer.
In the empty pot, heat 1 tablespoon oil and cook mushrooms over medium heat for 8 minutes until soft.
Add garlic, thyme, rosemary, sea salt, onion powder, tamari sauce, and broth. Whisk and cook until simmering and thickened, about 3-5 minutes. Turn off heat.
Mix drained veggies, cannellini beans, Greek yogurt, and 1/2 cup mozzarella cheese into the gravy mixture.
Spread the casserole mixture into the prepared dish.
In a medium bowl, combine crumbled crackers, 1 tablespoon oil, and remaining 1/2 cup cheese. Sprinkle over casserole.
Bake for 25 minutes.
Let cool for 10 minutes before serving. Garnish with fresh rosemary if desired.