In a food processor, pulse 1/3 cup almonds with sugar until finely ground. Coarsely chop remaining almonds.
In a bowl, mix breadcrumbs and milk. Add almonds and remaining ingredients, except oil. Mix until combined. Form into 1-inch balls.
Heat 1 1/2 tablespoons olive oil in a 12-inch heavy skillet over medium heat. Add half the meatballs, and saute until they are cooked through, about 7 minutes. Transfer meatballs to a platter. Repeat with the remaining oil and meatballs. Garnish with Parmesan, and serve immediately.