In a large bowl, stir together potatoes, onions, eggs, matzah meal, and salt.  

Line a baking sheet with two layers of paper towels. Heat enough oil to reach a depth of about 1/4-inch in a large skillet over medium-high heat. 

Form potato mixture into 3-inch round latkes, and fry in batches until browned and crisp, 4 to 6 minutes per side. Transfer to prepared pan. Continue making latkes with remaining mixture.  

While latkes cook, combine vinegar and sugar in a small saucepan; bring to boil over medium heat. Reduce to simmer; cook until reduced and thickened, 10 to 12 minutes. 

To assemble, place each latke on a small plate. Top each with one slice mozzarella, one slice tomato, and leaf or small sprig of basil. 

Garnish with drizzle of reduced balsamic, some evoo, and pepper to taste.