Preheat grill to high heat.
Lightly oil cooking grids.
Place mushrooms onto the grill, smooth side up.
Grill until they start to soften, about 10 minutes.
Turn over, and grill on the other side for about 5 minutes.
Meanwhile, heat olive oil and butter in a large skillet over medium heat.
Add the shallot and fry for a few minutes, stirring frequently.
Remove mushrooms.
Place mushrooms on a cutting board and slice.
Place mushrooms into the skillet and increase the heat to high.
Cook for about a minute, then pour in the wine.
Continue to cook and stir until the wine is nearly evaporated.
Remove from heat.
Serve.
