Preheat oven to 400°F. Spray a rimmed baking sheet with olive oil mister.
Place shiitake mushrooms on one side of baking sheet and place asparagus and garlic cloves on other side. Spray tops with additional olive oil. Bake for 10–12 minutes or until vegetables are softened and just beginning to brown. Remove from oven and cool slightly.
Transfer asparagus and garlic to food processor. Add almonds and olive oil. Pulse until finely chopped but not mashed; season with salt and pepper.
Preheat electric grill or panini press on high. Spread asparagus pesto on each half of ciabatta bread. Top four bottom pieces of bread with a quarter of the mushrooms and ¼ cup of cheese. Place other half of bread on top and press down.
Transfer panini to grill and close lid. Grill for about 5 minutes or until cheese has melted.
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