Combine mayonnaise, lemon zest, basil, and capers in a small bowl and mix well.

Cover the bowl and refrigerate for at least 1 hour to allow flavors to blend.

Prepare a medium-hot fire in a charcoal grill or preheat a gas grill to medium-high.

In a bowl, combine ground tuna, red bell pepper, green onion, Chardonnay, mustard, olive oil, and seasoning salt.

Mix the tuna mixture gently, adding just enough breadcrumbs to hold the mixture together.

Divide the tuna mixture into 4 equal portions and form into patties.

Brush the grill rack with vegetable oil.

Place the patties on the grill rack, cover, and cook, turning once, for 3-4 minutes on each side for medium-rare.

During the last few minutes of cooking, place the buns, cut side down, on the outer edges of the rack to toast lightly.

During the last minute of cooking, place 1 slice of cheese on each patty to melt.

Spread lemon-basil mayonnaise over the cut sides of the buns.

On each bun bottom, place an equal portion of artichoke hearts, a few greens, and a patty.

Add the bun tops and serve immediately.