Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
In a saute pan over medium-high heat, add the olive oil, sausage and shallots. Saute until browned, breaking up the sausage into small pieces with a wooden spoon, 5 to 7 minutes.
Add the browned sausage and reserved mushroom stems to the bowl of a food processor and pulse until combined. Add the pine nuts and pulse a few more times until slightly smooth. Transfer to a mixing bowl and fold in the Swiss cheese, Gruyere and cream.
Add the breadcrumbs and parsley to a small bowl and mix to combine.
Place the mushroom caps hollow-side up on the prepared baking sheet. Using a tablespoon, spoon the mushroom and sausage mixture into each mushroom cap. Top with the breadcrumb mixture. Bake until golden brown, about 20 minutes.