Preheat a grill or grill pan over medium-high. Drizzle the tuna with EVOO and season with salt and pepper.
In a large bowl, whisk the lemon juice, thyme, vinegar, mustard and garlic. Gradually whisk in 1/4 cup EVOO until the dressing is smooth; season. Add the kale, tomatoes, onion, beans, celery and parsley. Toss to coat; season again. Divide the salad among plates or shallow bowls.
Grill the tuna until cooked to desired doneness, 2 to 3 minutes per side for medium-rare. Slice the tuna and arrange on the salad.