In a food processor, pulse tomatoes until coarsely chopped.
Meanwhile, heat a large non-stick skillet over medium-high heat. Once heated, add the rutabaga noodles, season with salt and pepper and cook until wilted and cooked through, about 15 minutes. You may need to do this in batches. Once cooked, set aside in a large mixing bowl.
Place the skillet back over medium-high heat and add the oil. Once oil is shimmering, add the garlic and cook until fragrant, about 30 seconds. Add the tomatoes and bring to a boil. Lower the heat to medium and let cook at a solid simmer until sauce thickens, 12-15 minutes.
In the large mixing bowl with the rutabaga, add the prepared tomato sauce, basil, and half the mozzarella and toss to combine. Transfer the mixture to a 3-quart baking dish and top with the remaining cheese. Bake in the oven until cheese is golden and edges are bubbling, about 25 minutes.