Place a 10-inch skillet over high heat with butter and oil. As soon as you see that the butter foam has begun to subside, indicating it is hot enough, add the mushrooms. Toss and shake the pan for 4-5 minutes. During their saute the mushrooms will at first absorb the fat. In 2-3 minutes, the fat will reappear on their surface, and the mushrooms will begin to brown. As soon as they have browned lightly, remove from heat.

Toss the shallots of green onions with the mushrooms. Saute over moderate heat for 2 minutes.