Squeeze lemon juice in a large bowl. Add the rinds, and 6 cups of water. Peel salsify, trim the ends, and cut into 1/2-inch-by-2 1/2-inch long lengths. Place salsify in lemon water to keep it from browning.
In a large straight-sided skillet, heat soffrito over medium heat. Add garlic and rosemary, and cook, stirring occasionally, until garlic is golden and fragrant, about 5 minutes. Add tomato paste and crushed tomatoes with reserved juices. Season with salt and pepper. Cook until the flavors begin to meld, about 10 minutes.
Drain salsify, and place it into skillet with 1 cup water. Cover, and simmer over medium-low heat, turning occasionally, until tender, about 45 minutes. If the skillet begins to get dry, add a little more water. Adjust seasoning with salt and pepper. Garnish with basil, and serve.