Preheat a large nonstick skillet over medium-high heat with 3 turns of the pan of extra-virgin olive oil, about 3 tablespoons. Add the potatoes, parsnips, thyme and season with salt and pepper, stir frequently and cook for 10 to 12 minutes, or until the potatoes and parsnips are nice and tender and lightly browned. Add the minced onion and continue to cook until they are tender and the potatoes are nice and brown.
Once the hash is cooked, add the chopped parsley and lemon zest. Stir to combine and transfer hash to a serving platter. Serve it up.