Roast the poblano peppers over an open flame or in the oven until slightly charred. Cover with a towel to steam and soften. Cut into pieces and set aside. Puree sour cream, water, oil, garlic, and salt in a food processor. Add green onions and roasted poblano peppers, blend until desired texture.

Bring 4 cups of water to a boil. Stir in cornmeal and salt, reduce heat, and simmer for 5-10 minutes until thick. Mix in 1 tablespoon butter after cooking.

In a large skillet, melt 1 tablespoon butter over high heat. Add garlic and mushrooms, sauté until golden. Pour in the poblano sauce and add dissolved cornstarch. Simmer until sauce thickens. Serve mushrooms over the polenta.