3 slices white bread
1 large carrot, cut into 1/4-inch-thick rounds
1 celery, strings peeled, cut into 1/2-inch pieces
1/2 medium yellow onion, roughly chopped
2 cloves garlic, smashed and peeled
1/2 cup fresh flat-leaf parsley, leaves, loosely packed
1/2 cup plus 3 tablespoons ketchup
4 1/2 teaspoons dry mustard
8 ounces ground pork
8 ounces ground veal
8 ounces ground round
2 large eggs, beaten
2 teaspoons salt
1 teaspoon freshly ground pepper
1 teaspoon Tabasco Sauce, or to taste
1/2 teaspoon chopped fresh rosemary, plus more needles for sprinkling
2 tablespoons dark-brown sugar
1 tablespoon olive oil
1 small red onion, cut into 1/4 inch-thick rings