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Preheat oven to 350 degrees F.
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Baste mushrooms with 2 tablespoons of oil, salt liberally and place on a baking sheet. Bake in the oven for approximately 20 minutes, flipping the mushrooms after 10 minutes.
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While the mushrooms are roasting, heat 1 tablespoon oil in a saute pan over medium heat. Add shallots and saute for 2-3 minutes, until they start to caramelize. Add yams and 1/2 cup broth. Cover the pan and simmer until yams are soft (approximately 10 minutes), stirring occasionally.
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Place the yam and shallot mixture in a food processor, add the remaining 1/2 cup broth and blend until smooth. If you don't have a food processor, you can fork mash the mixture.
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In a saucepan, add peas and enough water to cover the peas. Bring to a gentle boil then drain the peas.
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In a mixing bowl, combine the yams and peas. Spoon the mixture into the Portobello mushroom caps and serve immediately.