Melt 1 1/2 teaspoon of butter with olive oil in a large skillet over medium heat. Cook and stir the portobello mushrooms, onion, carrot, and celery until the vegetables are softened and beginning to brown, about 8 minutes. Transfer the mushroom mixture to a large saucepan.
Pour the white wine into the skillet and bring to a boil, dissolving any browned flavor bits from the bottom of the skillet. Allow the wine to cook for about 2 minutes, until reduced, and pour into the saucepan. Stir the beef broth and tomato paste into the mixture in the saucepan, bring to a boil over medium-high heat, then reduce heat to low. Simmer, partially covered, until the beef broth has reduced and the vegetables are very tender, about 35 minutes.
Melt 1 teaspoon of butter in the original skillet, and cook and stir the enoki mushrooms until lightly browned, 3 to 4 minutes. Remove the enoki, and chop. Stir the chopped enoki mushrooms into the sauce and simmer for about 10 minutes; stir in the heavy cream, and allow to heat through (do not boil). Season with nutmeg, salt, and pepper to taste.
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