Put the shiitakes and the button mushrooms in a food processor that has been fitted with the metal blade.
Process until finely chopped.
In a large skillet, heat the olive oil ver moderate heat.
Add the shallot and garlic and saute until tender, 2 to 3 minutes.
Add the chopped mushrooms and saute, stirring frequently, until all the liquid from the mushrooms has evaporated and they have just begun to brown, 10 to 15 minutes.
Add the tomatoes, breaking them up with your hands.