1. Heat a large saute pan over medium heat. Add the olive oil and the diced onion. Season with salt and pepper and cook until tender, 3-5 minutes. Add the grated garlic and lower the heat. Add the mushrooms. Season with salt and pepper. Cook until the mushrooms are tender and a lot of the liquid has evaporated at the bottom of the pan, 5-8 minutes.
2. Add the Vermouth to the mushrooms and cook until the flavor of the alcohol has mellowed considerably, 5-8 minutes. Taste for seasoning. Add the sour cream and allow it to melt over low heat. Remove and reserve half (20) of the mushrooms.
3. Preheat oven to 350 degrees F. Preheat the broiler. When the mushrooms have cooled slightly, place half of them (20 mushrooms) on a flat surface and roughly chop to break them into smaller pieces. Toss them in a bowl with the Parmesan cheese, pecans and breadcrumbs.
4. A test run: Place a little bit of the stuffing on a baking sheet and place in the oven. Cook for a few minutes and taste for seasoning. Add more salt, cheese or even olive oil if the texture or flavor isn't quite where you want it to be. Fill each bottom of the reserved mushroom halves (remaining 20 mushrooms) with some of the stuffing. Don't be afraid to press and mold the stuffing on top of each mushroom.
5. Arrange the mushrooms on a baking sheet and bake in the oven until hot, 12-15 minutes. Place the mushrooms under the broiler for a minute or two until the tops brown. Serve immediately with a drizzle of Balsamic vinegar or lemon juice.