Arrange the baguette slices on a large baking sheet and drizzle or brush with olive oil. Sprinkle with a pinch of salt.
Broil the bread on low in an oven until golden and lightly toasted.
In a large pan, place the olive oil and butter over medium heat. Once heated, add the shallots. Cook, stirring occasionally, until softened.
Stir in the garlic and cook until just fragrant, 30 seconds to 1 minutes.
Add the mushrooms and cook, stirring occasionally, until browned.
Pour in the wine and scrape any browned bits from the bottom of the pan. Continue to cook until the wine has reduced completely. Season with salt, pepper, and the fresh thyme to taste and remove from heat.
Spread the mushroom mixture over the toasted baguette slices.
Top with a sprinkling of shredded fontina cheese. Place the baking sheet back under the broiler until the fontina is melted and bubbly.
Serve immediately and garnish with fresh parsley if desired.