Preheat the oven to 375 degrees Fahrenheit. Cut the *very* tops off of each of the tomatoes and use a spoon to scoop out the soft juicy pulp, while leaving the walls of the tomatoes intact. Place the tomato pulp in a bowl and set it aside, and set the hollowed out tomatoes aside and their caps/tops as well.

For the filling, heat the olive oil in a large pot over medium heat. Add the onions and cook until softened and transparent, about 8 to 10 minutes, stirring every few minutes. Add the garlic and allow to cook until the garlic is softened and fragrant, about 5 minutes more, stirring every minute or so. Add the eggplant and cook until it's softened a bit, about 5 to 7 minutes. Push the vegetables to the sides of the pan, leaving the center empty. Then add the ground beef or lamb to the empty center space, and sauté until cooked through, breaking the meat apart into small pieces with the end of your wooden spoon as it cooks.

Remove from heat and empty into a large heat-proof bowl (like a metal, glass, or ceramic one). Measure out two cups of the tomato pulp mixture and add it to the meat mixture. Add the rice, parmesan, basil, parsley, salt, and pepper and stir to combine.

In a small bowl, stir together the breadcrumbs, salt, garlic powder, and thyme. Drizzle with the olive oil and stir it up with a fork to lightly coat the breadcrumbs in the oil. Set it aside.

Evenly spread out 1/4 of the meat mixture on the bottom of a greased 9 x 13-inch casserole or baking pan. Place the six hollowed out tomatoes in the pan, and fill them with the meat mixture. Place any remaining meat mixture between the outside of tomatoes in the pan, filling up any crevices and gaps between the stuffed tomatoes. Pour the chicken stock into the pan.

Sprinkle the breadcrumb mixture over the filling in each of the tomatoes, and sprinkle it on the filling between the tomatoes in the pan. Place the caps on the tomatoes and, using a pastry brush, lightly brush the tops of the caps and any exposed skin of the stuffed tomatoes with some olive oil. Place the pan in the oven and bake until the tomato caps get golden patches and the filling is bubbling and fragrant, about 45 to 55 minutes. Remove from the oven and serve.