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.