Sort the mushrooms, setting aside the largest for stuffing and removing the stems. The smaller mushrooms will be used for the filling. (I used six ounces of small ones.)

Combine the onion and small mushrooms in the bowl of a food processor. Pulse until finely diced.

Heat oil in a sauté pan over medium heat. Add onion/mushroom mixture and garlic and sauté five  to seven minutes. Stir in basil. In a medium bowl, combine mixture with veal and season with salt and pepper.

Place the egg in a small bowl. Place the breadcrumbs in a second small bowl. Stuff each mushroom with a mound of the veal mixture. Dip into the egg and then the breadcrumbs.

Heat oil in a sauté pan over medium-high heat. Add mushrooms, stuffing side down, and fry until breadcrumb topping is crispy and golden, about three to four minutes. Remove to a baking pan.

Preheat oven to 350 degrees Fahrenheit. Add olive oil and vinegar to the baking pan under the mushrooms. Season with additional salt and pepper. Bake for 20 minutes, until mushrooms are cooked through.