Place potatoes and parsnips in a large pot and submerge in cold water (there should be at least 1 inch of water over the vegetables). Salt water well. Bring to a boil and then reduce to a simmer and allow potatoes and parsnips to cook for approximately 25-35 minutes, or until both vegetables are very fork tender. Drain, return the vegetables to the pot, and add 2/3 cup milk, 2 tbsp olive oil, and salt and pepper to taste. Mash well with a potato masher. If you need more milk, add the remaining 1/3 cup. Set the mashed potatoes and parsnips aside.

While potatoes are cooking, bring 1 1/2 cup lentils and 3 cups water to a boil. Reduce and simmer until lentils have absorbed all liquid, and are soft (about 30 or 35 minutes). Set lentils aside.

Heat 2 tbsp olive oil in a large saute pan over medium. Add onions and garlic and cook until onions are translucent and golden (10 minutes or so). Add the carrots and celery and cook till both vegetables are tender (another 8 minutes). Add the cremini mushrooms and cook for another 3 minutes before adding the lentils, the rosemary, the thyme, and 1/2 cup vegetable broth. Simmer the mixture, stirring well to incorporate flavors. Add more liquid as needed: you don’t want there to be too much broth or liquid in the bottom of the pan, because you’ll get a runny shepherd’s pie, but you do want it to be quite moist. When everything is warm and well mixed, season to taste with salt and pepper.