Melt 2 tablespoons of butter in a heavy large saucepan over medium-high heat.
Add the onions and mushrooms and saute until tender, about 5 minutes.
Season with salt. Add the garlic and oregano and saute until fragrant, about 30 seconds.
Stir in the tomato paste and cook for 2 minutes, stirring constantly.
Whisk in the wine. Simmer until the sauce reduces by half, stirring occasionally, about 10 minutes.
Remove the skillet from the heat. Cut the remaining 4 tablespoons of butter into small ½-inch chunks and whisk in the sauce a little at a time. Season the sauce, to taste, with salt and pepper.