Preheat the oven to 400 degrees F.
Coat a large saute pan with olive oil, add the pancetta, and bring to medium-high heat. Cook the pancetta until it starts to brown and crisp on the edges, 6 to 8 minutes. Add the onions and season with salt. Continue cooking until the onions are soft and aromatic, about 5 minutes. Add the chopped mushroom stems, rosemary and garlic, and cook for another 2 to 3 minutes, stirring frequently. Remove from the heat and place in a mixing bowl to cool.
Once cooled, add the sausage and breadcrumbs. Pour in 1 whisked egg and combine. Add another egg if the mixture is still dry.
Make a 1- to 2-inch tester patty out of the stuffing mixture. In a small saute pan, heat a bit of oil and cook the patty until it's done. When cool enough, taste your tester patty to make sure it's delicious, if it's not, re-season.
When your tester tastes fabulous, generously fill each mushroom cap with the stuffing mixture and arrange them on a rimmed baking sheet. Pour 1/4 to 1/3 cup water into the pan to keep the mushrooms moist. Bake until the filling is cooked through and brown and crispy on the top, 8 to 10 minutes. Transfer to serving platters.