In a large pan over medium heat add 2 tablespoons olive oil. Add the garlic and fry for less than 1 minute, until starting to sizzle. Add the tomatoes and any juice, chard, and kale to the pan and ¾ of a teaspoon salt. Stir through. Cover the pan and continue to cook for 20 minutes, stirring every once in a while, until the kale and the chard are wilted, and the tomatoes have broken down.
Meanwhile, bring a large pot of salted water to a boil and cook the pappardelle pasta according to packaging directions. Drain and place on a plate and add the 1 tablespoon remaining olive oil and mix well. Place on a serving dish.
Remove from the heat the kale chard combination and add the spinach, lemon juice, lemon zest, and parsley and pour over the pasta.