Preheat oven to 425° F.
On a lightly floured surface with a floured rolling pin roll out pastry into a rectangle roughly 17 by 15 inches and trim edges to form a 16- by 14-inch rectangle.
Cut pastry in half lengthwise, forming two 16- by 7-inch rectangles.
Brush edges with water and fold in edges to form a 1/2-inch-wide border on each rectangle.
With tines of a fork press border to seal.
Transfer rectangles to a large baking sheet.
Thinly slice tomatoes.
Halve onion lengthwise and thinly slice.
Divide anchovy paste between rectangles and spread in a very thin, even layer.
Sprinkle each tart evenly with 1/2 cup mozzarella and 2 tablespoons Parmesan.
Arrange tomato slices in one layer on cheese.
Scatter onion slices and herbs over tomatoes and sprinkle with remaining 1/4 cup Parmesan and salt and pepper to taste.
Bake tarts in upper third of oven 12 to 15 minutes, or until crust is golden.
Tarts may be made 2 days ahead and chilled, covered loosely.
Crisp tarts in oven before serving.
Serve tarts warm or at room temperature.