Preheat oven to 350 F. Coat the bottom of the a baking pan with 1-tablespoon of olive oil.
Using a chef's knife. Slice the eggplant in half lengthwise. Using a spoon or scoop, remove most of the eggplant flesh, leaving the skin intact. Place hollowed out eggplant skin in prepared baking pan. Chop scooped out flesh, and set aside.
In a saute pan, heat 2 tablespoons of oil over medium heat. Add chopped eggplant, and saute for 3 to 4 minutes. Add zucchini and saute for 2 additional minutes. Remove eggplant and zucchini from pan, and set aside. Heat remaining oil over medium heat. Add onion and garlic and saute 4 to 5 minutes until onions are translucent. Stirring frequently, add mushrooms, and saute an additional 5 to 7 minutes until tender. Add rice, and saute 4 to 5 minutes. Add diced tomatoes, and stir to combine. Stirring frequently, allow the rice mixture to cook 2 to 3 minutes. Add broth and stir to combine. Reduce heat to simmer, cover and cook for 40 to 45 minutes until rice is tender. Fluff cooked rice with fork. Stir in zucchini and chopped eggplant, red pepper flakes, thyme, and salt and pepper to taste.
Divide the rice and vegetable mixture between the two hollowed-out eggplants, mounding the mixture in the shell. Cover with aluminum foil and bake in preheated oven 35 to 40 minutes until eggplant is soft. Makes 2 servings.