Lay the baguette slices out on a straight-sided baking sheet. Brush each slice of baguette with a generous amount of olive oil. Sprinkle evenly with salt and bake until golden brown and crispy, about 8 minutes. Remove the crostini from the tray and set aside to cool.
While the crostini bake, combine the mascarpone, chives and salt in a small bowl. Set aside.
Increase the oven temperature to 500 degrees F.
On the same baking sheet, combine the mushrooms, red grapes, thyme leaves, shallots, olive oil and salt. Toss well to coat and combine. Roast until the mushrooms are beginning to brown and the grapes have released some of their juices, 8 to 10 minutes Scrape the contents of the tray into a medium bowl and toss with the sherry vinegar. Cool to room temperature.
To serve, spread each crostini with equal amounts of the mascarpone mixture. Spoon a small amount of the mushroom mixture on top of each crostini. Top each with one shaving of Parmesan.