Add olive oil and butter to a 10- to 12-inch frying pan over medium-high heat. Add shallots and stir often until limp, about 2 minutes. Add rinsed and drained fresh morel or sliced common mushrooms (halve smaller morels; quarter larger ones); stir just until they begin to release their juices, 1 to 2 minutes. Add dry sherry and stir often until evaporated. Add salt and pepper to taste. Pour mushrooms into a small bowl and stir in 1 tablespoon white truffle oil (optional). Let stand for at least 1 hour or cover and chill up to 1 day.