01 - Heat BBQ grill or grill pan to medium-high temperature (approximately 400°F).
02 - Whisk together olive oil, lemon zest, minced garlic, sea salt, and black pepper in shallow dish. Coat barramundi fillets thoroughly and marinate for 10 minutes at room temperature.
03 - Lightly brush cos lettuce leaves with olive oil, ensuring even coating for grilling.
04 - Place lemon halves cut-side down and halved jalapeños on grill. Cook 3-4 minutes until charred and softened. Remove to cool briefly. Finely chop jalapeños and squeeze juice from grilled lemons.
05 - Combine mayonnaise, grilled jalapeños, 2 tbsp grilled lemon juice, capers, dill, parsley, diced shallot, Dijon mustard, salt, and pepper in bowl. Mix thoroughly and refrigerate until assembly.
06 - Place marinated fillets on grill. Cook 3-4 minutes per side until fish flakes easily with fork and develops light char marks. Internal temperature should reach 145°F.
07 - Grill cos lettuce leaves 1-2 minutes per side until slightly wilted with smoky flavor and grill marks.
08 - Lightly toast split brioche buns on grill for 30-60 seconds until golden and warm.
09 - Spread grilled lemon jalapeño tartare on both cut sides of each bun. Layer with grilled cos lettuce, barramundi fillet, tomato slices, and cucumber. Top with bun crown.
10 - Serve immediately while fish is hot and lettuce maintains slight crunch.