Allow tuna to come to room temp. Preheat grill to high.
In a medium bowl, combine all ingredients for the dressing except the olive oil. Wisk the oil in a drizzle at a time to desired consistency (the same as you would for a vinaigrette). Set aside.
Lightly brush tuna with olive oil and season with salt and fresh ground pepper. Grill tuna to 125 degrees F internal temp. Allow to cool slightly. Break the meat up into large flakes and coat with the dressing.
Serve with crackers, toasted bread, or as a sandwich.