Cook the rice according to the package directions.
While the rice cooks, heat the oil in a large skillet over medium. Add in the onion and sauté until translucent, about 5-7 minutes. Add in the garlic, mushrooms, red pepper flakes, thyme, basil, pepper, and salt. Sautee until the mushrooms are cooked, bout 7-10 minutes. Set aside.
In a small saucepan add in all of the sauce ingredients. Over medium heat, bring the sauce to a simmer. Cover and simmer for 5 minutes. Set aside.
Add the cabbage leaves to a large bowl. Fill the bowl with boiling water and cover the bowl with a plate, lid, or even a cookie tray. Let sit for 10 minutes so the cabbage softens and becomes easier to roll.
While the cabbage sits, coat the bottom of a 9x13 inch baking dish with a thin layer of the sauce. Combine the mushroom mixture, 1/2 cup sauce, and cooked rice.
Grab a cabbage leaf, shaking off the excess water and add 2-4 tablespoons of the filling mixture (more for larger leaves, less for smaller) to one end of the cabbage leaf. Roll the leaf up like a burrito, tucking in the sides. Line up filled and rolled leaves in the baking dish. Continue rolling and adding to the baking dish until all the leaves are filled. Cover with the remaining sauce and bake at 350 for 40-50 minutes or until the rolls are warmed through. Serve.