Place the parsnips, garlic, potatoes and celery root in a large pot. Cover with cold water by one inch and add the 2 tablespoons salt. Bring to a boil over high heat. Reduce the heat to medium and simmer until the vegetables are tender, 10 to 15 minutes. Drain well, then return the cooked vegetables to the pot. Using a wooden spoon, stir the vegetables over medium heat to remove some of the excess moisture, about 4 minutes. With a large fork or potato masher, lightly mash the vegetables. Off the heat, add the 1 teaspoon salt and the lemon zest, thyme, olive oil and Parmesan. Mix until well combined. Serve hot.