Preheat oven to 375 degrees. In a large skillet, heat oil over medium. Add sausage and cook, breaking up with a wooden spoon, until no longer pink, 3 to 5 minutes. Remove stems from mushrooms, trim ends, and finely chop. Add chopped stems, hazelnuts, garlic, shallot, and rosemary to sausage; season with salt and pepper. Cook until vegetables are tender, 4 to 6 minutes; transfer to a bowl and set aside to cool.
To cooled sausage mixture, add egg and breadcrumbs; stir to combine. Place mushroom caps on a large rimmed baking sheet and season cavities with salt and pepper. Stuff caps with sausage mixture, packing tightly.
Bake mushrooms until tops are browned and caps are tender, 25 to 30 minutes. Sprinkle with additional rosemary before serving.
Look for blanched (or skinless) hazelnuts at the supermarket. If you canÂ‚'t find them, bake hazelnuts with the skin still on at 350 degrees until skins crack. Rub the nuts in a kitchen towel to remove the outer layer. You can make the mushrooms ahead through step 2; cover and refrigerate up to a day. Increase baking time by about 5 minutes.