Heat a large pot on medium heat with olive oil. Dice carrots, onion, and drained tofu into small cubes and add to the pot along with the ground thyme. Sautee for 5-7 minutes.
In the meantime, dice the ½ of a butternut squash into slightly larger cubes (about 3 cups total). Add the diced squash to the pot with the vegetable broth and mushrooms and let it simmer together for 10-12 minutes, avoiding a hard boil but allowing some liquid to evaporate. Turn off the heat when the butternut squash can be pierced with a fork.
While the butternut squash is cooking, add the cauliflower florets and 2 tablespoons of water into a microwave safe bowl and microwave for 6 minutes. Stir and microwave for another 6 minutes until soft.
Puree the cauliflower in a food processor until creamy, adding the grated Parmesan or nutritional yeast for flavor. Set aside.
Stir the cornstarch into 2 tablespoons of cold water until smooth, and add to the main pot of filling. Stir for a few minutes until thickened and taste, adding salt and pepper as desired.
Ladle the filling mixture into a 2-quart baking dish. Carefully spread the pureed cauliflower mixture on top of the filling along with salt and pepper.
Bake the shepherd's pie for 30 minutes, until bubbling (slide a cookie sheet on the rack below to catch any spills). Allow it to cool for 10 minutes before serving.
Notes
For vegan option: Sub 2 tablespoons of nutritional yeast for the parmesan in the cauliflower mash.
Recipe by Uproot Kitchen at https://uprootkitchen.com/2014/11/14/vegetarian-shepherds-pie/