Heat the oven to 400°F (200°C). Arrange the 16 baguette slices on a baking sheet and brush both sides lightly with about 2 tablespoons of the olive oil.

Toast the bread for 6 to 8 minutes, turning once, until the slices are crisp and lightly golden. Remove the toast from the oven and keep it nearby for assembly.

Heat the remaining olive oil and the butter in a large skillet over medium-high heat. Add the sliced mushrooms and cook for 6 to 8 minutes, stirring occasionally, until their moisture has evaporated and the mushrooms are browned.

Add the minced shallot, garlic, thyme, kosher salt, and black pepper. Cook for 2 minutes, stirring often, until the aromatics smell fragrant and the shallot begins to soften.

Pour in the white wine or stock and cook for 1 to 2 minutes, scraping up the browned bits from the skillet, until the liquid is nearly evaporated. Stir in the lemon juice, if using, and the chopped parsley.

Spoon the mushroom mixture onto the toasted baguette slices, dividing it evenly among all 16 pieces. Top each bruschetta with finely grated Gruyère.

Return the assembled bruschetta to the oven and bake or broil until the cheese melts and turns lightly golden, about 3 to 5 minutes in the oven or 1 to 2 minutes under a broiler. Serve hot.