Begin with the filling. Chop the young onions, slice the smoked bacon into small pieces, and crush the garlic. If you’re using whole mozzarella, grate it finely. Preheat your oven to 350°F/180°C.
Warm a bit of oil in a frying pan and sauté the onions for a couple of minutes, just until they soften and turn glossy. Set aside to cool slightly.
Clean the parasol mushrooms carefully without rinsing them in water. Brush off any dirt, pine needles, or leaves using your hands or a soft brush.
Prepare a baking tray lined with parchment paper and arrange the mushrooms on top. Lightly season with salt and black pepper, and tuck a few pieces of garlic between the gills.
Place the tray in the oven for a few minutes; just long enough for the mushrooms to release a bit of moisture and become pliable. If they release too much liquid, gently press it out with your hands.
Spoon the filling onto one side of each mushroom cap, then roll it carefully. Tuck in the edges to keep the filling inside and form a firm, compact roll.
Set up three shallow bowls or plates. Add flour to one, whisked eggs to another, and breadcrumbs to the last. Roll each mushroom first in flour, then dip it in the egg, and finally coat it thoroughly in breadcrumbs.
Heat oil in a large skillet over medium heat. Once the oil is ready, add the rolls and fry them until golden on one side. Turn and fry the other side until both are crisp and evenly browned.
Serve the cheesy mushroom rolls warm while the mozzarella is still melted and creamy.