Preheat oven to 350ºF. Lightly grease a large, rimmed baking sheet. Remove stems from mushrooms and chop. Place mushroom caps, stem sides up, on prepared baking sheet.
Heat oil in a large skillet over medium heat. Add shallot and garlic. Season with salt and pepper. Cook, stirring occasionally, until tender, 3 to 4 minutes. Add chopped mushroom stems and season with salt and pepper. Cook, stirring, until starting to brown, 7 to 9 minutes. Add sausage and cook, breaking it into small pieces with a wooden spoon, until browned and cooked through, 5 to 6 minutes; transfer to a bowl.
Add parsley, lemon zest and juice, thyme, panko, and Parmesan, and stir to combine. Fill mushroom caps with filling. Bake until mushrooms are tender, 28 to 30 minutes. Serve immediately.