Marinate the tuna: Place the tuna in a shallow dish and pour the soy sauce over the top. Turn the tuna so all the sides of tuna steaks are coated well. Refrigerate for 30 minutes.
Prep the ingredients: Remove the ribs from the kale and discard. Chop the kale leaves into bite-size pieces. Cube the bread.
Transfer the kale to a large bowl. Add 1 tablespoon of the oil to the kale and massage the oil into the leaves by scrunching with your hands. Continue the process until the leaves are well coated. Set aside.
Make the Caesar dressing: Whisk together the mayonnaise, garlic, lemon juice, Dijon mustard, Worcestershire sauce, ½ cup Parmesan cheese, and salt and freshly ground pepper to taste in a medium bowl. Refrigerate until ready to serve.
Toss the bread cubes with the remaining oil in a medium bowl. Transfer to a grill basket. Remove the tuna from the marinade.
Heat the grill to medium-high heat until hot. Add the grill basket to one side of the grill and the tuna steaks to the other. Grill the tuna 1-2 minutes on each side or to desired doneness. Grill the bread cubes, stirring frequently, until charred and toasted.
Remove the tuna and grill basket from the grill. Let the bread cool and the tuna rest before slicing. To serve, combine the kale, romaine, and croutons in a large bowl. Drizzle desired amount of dressing over the salad and toss well to coat. Sprinkle with more Parmesan cheese. Divide the salad between 4 serving plates or bowls. Top each with tuna and serve.