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 to a cutting board, and slice.
Place 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.