Melt 3 tablespoons of butter in a heavy skillet over high heat. Add mushrooms and onions; saute until golden brown, about 10 minutes. Mix in Sherry; cook 1 minute. Remove from heat. Mix sour cream and thyme. Season to taste with salt and pepper. Set aside.
Whisk eggs, salt and pepper in a large bowl to blend.
Melt 1 teaspoon of butter in a 6-inch skillet over low-medium heat. Pour generous 1/3 cup egg mixture into skillet and cook until almost set, tilting skillet and lifting egg mixture with spatula to allow uncooked portion to run underneath, about 1 minute. Spoon 1/3 cup mushroom mixture over half of the omelet. Sprinkle mushroom mixture with 2 1/2 tablespoons of crumbled blue cheese.
Cover and cook until cheese melts, about 2 minutes. Fold unfilled half of omelet over filling. Slide omelet out onto plate. Repeat with remaining butter, egg mixture, mushroom filling and cheese forming total of 6 omelets.