For the crostini, preheat oven to 350°F. Brush baguette slices lightly with butter. Bake until toasted and lightly browned, 4 to 5 minutes per side. Lightly season with salt and spread with chèvre.
For the ragoût, heat olive oil in a sauté pan over medium heat. Add garlic and shallot and cook until translucent, 1 to 2 minutes. Do not let garlic brown. Add half of the thyme and all mushrooms. Season with salt and pepper. Let mushrooms cook over medium-high heat without excessive stirring so they will brown.
Once mushrooms are browned and tender, 5 to 7 minutes, add sherry vinegar and reduce until the pan is dry. Combine cornstarch in sherry wine, mix until dissolved and add to the pan. Cook until reduced or until there is very little liquid left in the pan.
Remove from heat and stir in crème fraîche. Taste and adjust seasoning with salt and pepper. Place a tablespoon of ragoût on each crostini and spread to cover the entire toast. Garnish with remaining chopped thyme and serve warm.
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