Bring a large pot of salted water to a boil. Carefully remove the core from the cabbage and lower the whole head into the boiling water. As the outer leaves soften, gently peel them away with tongs and transfer them to a plate. Repeat until you have 12 to 14 large leaves. Pat them dry.
Heat the olive oil in a large skillet over medium heat. Add the onion and carrot and cook for about 5 minutes until softened.
Stir in the garlic and mushrooms. Cook for another 6 to 8 minutes until the mushrooms release their moisture and begin to brown.
Mix in the tomato paste, smoked paprika, thyme, oregano, salt, and pepper. Cook for 1 minute.
Add the cooked lentils, cooked rice, and parsley. Stir until everything is evenly combined, then remove from the heat and let the filling cool slightly.
Preheat the oven to 375°F (190°C).
For the sauce, heat the olive oil in a saucepan over medium heat. Add the garlic and cook for 30 seconds. Stir in the crushed tomatoes, vegetable broth, tomato paste, smoked paprika, basil, maple syrup, and soy sauce. Simmer for 10 minutes, then season to taste.
Spread about 1 cup of the tomato sauce across the bottom of a 9×13-inch baking dish.
Lay a cabbage leaf flat. Trim the thick rib if needed. Place about ¼ cup of filling near the base of the leaf. Fold in the sides and roll tightly into a neat bundle.
Arrange the cabbage rolls seam-side down in the prepared baking dish. Repeat with the remaining filling and cabbage leaves.
Pour the remaining tomato sauce evenly over the rolls. Cover the dish tightly with foil and bake for 60 minutes.
Remove the foil and bake for another 15 minutes until the sauce is bubbling and the cabbage is completely tender. Let the rolls rest for 10 minutes before serving. Garnish with fresh parsley and enjoy.