Whisk olive oil, lemon juice, Dijon, chopped capers and pepper in a bowl. Add 1/3 cup of the drained beans and mash them into the dressing with a fork.
Flake drained tuna gently, then fold it into the mashed-bean dressing with remaining whole beans and parsley. Keep some fish flakes intact.
Cover and refrigerate for 20 minutes until cold; this chilling time is included in prep time.
Divide arugula among the ciabatta bottoms and spoon the tuna salad evenly over it. Close with the roll tops and cut each sandwich across the middle.
Serve cold or refrigerate at 40°F or below, using ice packs when taking the sandwiches away from home.