Preheat the oven to 350°. On a rimmed baking sheet, toss the shaved parsnips with the extra-virgin olive oil and season with salt and pepper. Roast for about 20 minutes, tossing once, until the parsnips are tender and starting to crisp around the edges. Let the parsnips cool slightly.
Preheat the broiler. Arrange the sourdough bread slices on a medium baking sheet. Spread equal amounts of the crème fraîche on each bread slice, then top with the pear slices, roasted parsnips and cheese. Season the tartines with salt and pepper. Broil the tartines 8 inches from the heat for about 3 minutes, until the cheese is melted. Serve the tartines hot.