01 - Preheat BBQ grill or indoor grill pan to medium-high heat, approximately 375-400°F.
02 - In a shallow dish, whisk together 2 tbsp olive oil, lemon zest, minced garlic, sea salt, and black pepper. Add barramundi fillets and turn to coat evenly. Let marinate for 10 minutes at room temperature.
03 - Brush cos lettuce leaves lightly with 1 tbsp olive oil on both sides.
04 - Place lemon halves cut-side down and jalapeño halves on the preheated grill. Cook for 3-4 minutes until lemons are charred and jalapeños are softened with blistered skin. Remove from heat and let cool slightly.
05 - Finely chop the grilled jalapeños. Squeeze approximately 2 tbsp juice from the charred lemons. In a medium bowl, combine mayonnaise, grilled jalapeños, grilled lemon juice, capers, dill, parsley, diced shallot, and Dijon mustard. Season with salt and pepper to taste. Refrigerate until assembly.
06 - Place marinated barramundi fillets on the grill. Cook for 3-4 minutes per side, until fish is opaque throughout, flakes easily with a fork, and has light char marks. Avoid overcooking to maintain moisture.
07 - Place prepared cos lettuce leaves on the grill. Cook for 1-2 minutes per side until slightly wilted with smoky char marks. Remove from heat.
08 - Lightly toast burger buns on the grill, cut-side down, for 30-60 seconds until golden and crisp.
09 - Spread grilled lemon jalapeño tartare generously on both cut sides of each bun. On the bottom bun, layer grilled cos lettuce, followed by a barramundi fillet, 2 tomato slices, and 2 cucumber slices if using. Top with the remaining bun half.
10 - Serve immediately while fish is hot and lettuce retains its smoky texture. Pair with crisp white wine or pale ale if desired.