Seed tomato and chop fine. In a bowl stir together tomato, olive paste and basil. Cut mozzarella into thin slices. Coarsely chop arugula and, in a bowl, toss with oil, salt and pepper to taste.
Halve focaccia horizontally and spread bottom half with olive mixture. Top olive mixture with mozzarella, prosciutto, arugula and remaining focaccia half. Press focaccia gently and cut lengthwise in half and crosswise into thirds to make 6 sandwiches. Cut sandwiches diagonally in half and wrap tightly in plastic wrap. Chill sandwiches at least 1 hour and up to 1 day.