Prepare Crostini: Preheat the oven to 375°F (190°C) with a rack in the center position. Place the bread slices on a large baking sheet and toast for 10 to 15 minutes or until golden brown. Remove and allow to cool.
Roast Mushrooms: Increase the oven heat to 475°F (250°C). Slice the shiitake mushrooms caps into ½-inch thick slices. Spread mushrooms onto a half sheet pan. Toss with the olive oil, the sliced garlic, rosemary sprigs (breaking them apart slightly with your hands), and a generous seasoning of salt and pepper, and
Roast the mushrooms for 12 to 18 minutes, tossing once or twice with a wooden spoon. Remove and allow to cool in pan on rack until lukewarm. Discard rosemary sprigs.
Prepare Whipped Ricotta: Place ricotta and olive oil in bowl of a small food processor. Process for 10 to 15 seconds until smooth. Stir in the grated cheese and season with salt and pepper to taste.
Assemble: Spread each toasted baguette slice with the whipped ricotta and top with a spoonful of roasted mushrooms. Optional: Drizzle with balsamic glaze. Serve immediately.