Heat 1 tablespoon oil in large nonstick skillet over medium heat.
Add onions and rosemary and cook, stirring occasionally, until lightly browned, about 12 minutes; remove to a bowl.
Return the pan to the stove and add half the remaining oil. When it's hot, add the portabella mushrooms and sauté until nicely browned, about 5 minutes.
Add portabellas to the onion mixture and repeat, sautéing with the remaining oil and the white mushrooms.
Return everything to the pan and add the tomatoes, tomato paste, garlic, 1½ cups water and vinegar.
Simmer gently for 12 to 15 minutes, then swirl in the butter. Season with salt, pepper and red pepper flakes.
Serve, and enjoy!