Put the arugula greens into a large serving bowl and set aside.
In a large saute pan over medium-high heat, add the butter. Add garlic and shallots and cook until fragrant, about 1 to 2 minutes. Add the mushrooms and saute until nicely caramelized, about 3 to 4 minutes. Season with salt, pepper, and stir in the sherry vinegar. Remove from heat and stir in the mascarpone until the mixture becomes creamy. Add the parsley and set aside to cool to room temperature
Pour the mushroom mixture over the arugula greens and serve.