Preheat oven to 350 F.
Prepare mushrooms: If needed, clean mushrooms by gently brushing with a pastry brush or wiping with a damp cloth. Remove stems, saving them for stock.
Prepare puree: Heat 2 tablespoons olive oil in a medium size sauté pan over low heat. Add sweet potatoes and cover. Stir often. After sweet potatoes have softened, about 15-20 minutes, puree with a food mill or a food processor. (Alternatively, peel and cut root vegetables into large pieces. Cook in salted boiling water until tender. Puree in a food mill. Mix in a tablespoon of melted butter, olive oil or a light cream.)
Make pesto: In a food processor, add kale, extra-virgin olive oil, nutritional yeast, garlic, lemon juice and salt. Process until smooth. Add walnuts and pulse until desired consistency. Taste, season with additional salt and lemon juice as needed.
Line a large baking sheet with parchment paper. Spoon puree into mushrooms and place on parchment. Place in preheated oven, and bake until tender, 10-15 minutes.
Garnish stuffed mushrooms with pesto and serve immediately. They are great with spicy kale chips (see separate recipe).