Cook potatoes in boiling salted water until tender and drain. Return to pot and cover to keep warm while preparing mushrooms.
In a sauté pan over medium high heat, melt butter and heat oil. Add mushrooms and shallots and sauté until moisture has evaporated, about 5 minutes.
Add garlic and thyme and sauté one minute more. Add vermouth and cook until absorbed. Remove from heat.
Roughly mash potato and sour cream with a fork. Stir in mushroom mixture and Asiago and season to taste. Set aside until ready to serve.
To serve, preheat oven to 400 F. Spoon potato mixture onto toasted baguette slices. Heat for about 7 minutes, until warmed through. Serve warm or at room temperature.
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