Preheat the oven to 400 degrees F, if desired (oven optional).
Heat 2 tablespoons of the olive oil in a large oven-proof saute pan over medium-high heat. When the oil is hot, add the shallot and cook for 30 seconds. Add the asparagus and cook for 3 minutes. Push the asparagus to one side of the pan, and add the remaining 1 tablespoon olive oil and the shiitake mushrooms. Cook for 3 to 4 minutes, allowing the mushrooms to brown. Add the tomatoes and thyme, and cook for another 2 minutes, tossing the ingredients together to combine.
If roasting in the oven, transfer the pan to the oven and cook for 3 to 4 minutes, or until the asparagus is crisp-tender, if desired
Transfer the asparagus mixture to a serving platter, garnish with the cheese, and serve immediately.