1. Combine wine, lemon juice, shallots, and garlic in saucepan. Place over high heat; bring to a boil. Reduce heat to medium; simmer until liquid is reduced to 1/4 cup, about 10 minutes. Strain into small bowl; discard solids.

2. Whisk butter into liquid; add anchovies and capers. Roughly chop 1 1/2 cups basil; add to liquid. Adjust seasoning. Boil water in small saucepan, remove from heat, and place bowl of sauce over it to keep sauce warm.

3. Arrange mozzarella over four slices of bread. Scatter remaining 1/2 cup basil over cheese, and cover with remaining bread.

4. Heat 1 tablespoon oil in skillet over medium-high heat; arrange two sandwiches in skillet. Cover with sheet of foil. Place heavy skillet over foil; set a tea kettle filled with water in skillet as a weight. Cook until golden and cheese is starting to melt, 3 to 4 minutes. Turn sandwiches; cook other side with weight in place until golden and melted, 2 to 3 minutes more. Keep warm in oven while making remaining sandwiches. Arrange frisee on platter, and cut sandwiches into triangles; place over frisee. Drizzle with sauce. Serve with remaining sauce on the side.