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Step 1
For the polenta, bring 4 1/2 cups water and the milk to a high simmer in amedium-size heavy saucepan set over medium-high heat. Add salt. Pour thecornmeal slowly into the liquid, stirring with a wire whisk to prevent clumping. Continue stirring as the mixture thickens, 2 to 3 minutes.
Step 2
Turn heat to low. Cook for approximately 40 to 45 minutes, stirring every 5 to 10 minutes. If the polenta becomes quite thick, thin it with 1/2 cup water, stir well and continue cooking. Add up to 1 cup more water as necessary, to keep the polenta soft enough to stir.
Step 3
Add the butter to pot, and stir well. Add the Parmesan, if using. Taste forseasoning. Set the covered saucepan in a pot of barely simmering water,and keep warm for up to an hour or so.
Step 4
Meanwhile, put the dried mushrooms in a small bowl, and cover with about1/2 cup boiling water. Allow to steep for 20 minutes. Remove the mushrooms, and pat dry, then chop roughly. Reserve the mushroom stock.
Step 5
Melt 2 tablespoons of the butter in a sauté pan set over high heat until it hasmelted. Add the garlic and cook until it starts to sizzle, about 30 seconds. Do notlet the garlic brown.
Step 6
Add the fresh and reconstituted mushrooms and thyme to the pan, andsauté 3 to 4 minutes, turning until browned. Add about 1/4 cup of themushroom stock to deglaze the surface, using a wooden spoon to scrapeat the browned bits. Allow the stock to reduce by half, then turn the heatto medium-low and add the remaining 3 tablespoons of butter, whiskingto combine, followed by the soy sauce, cream and olive oil. Allow mixture tocook until it thickens a little, then remove from heat. Taste for seasoning, adding black pepper, if desired.
Step 7
Put the polenta in a warmed bowl, then top with mushrooms and the sauce.Serve immediately.