In a small skillet over medium heat, sauté shallots and garlic in a little EVOO to soften. Cool completely.
Place tuna in food processor and pulse into coarse ground meat. Place tuna in a bowl and add shallots and garlic, Herbes de Provence, fennel, celery seed, salt and pepper. Form 4 patties and reheat skillet over medium-high heat with a drizzle of EVOO. Add tuna burgers to the pan and cook 3 minutes on each side for pink centers and 5-6 minutes to cook through. Top patties with cheese after they are flipped, loosely tent pan with foil to melt cheese.
Combine Dijon or Dijonaise with capers in a small bowl.