01 - Preheat BBQ grill or grill pan to medium-high heat (375-400°F).
02 - In a shallow dish, whisk together 2 tablespoons 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 - Lightly brush cos lettuce leaves with 1 tablespoon 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 deeply charred and softened. Remove from heat, let cool slightly. Finely chop grilled jalapeños and squeeze juice from grilled lemons.
05 - In a medium bowl, combine mayonnaise, chopped grilled jalapeños, 2 tablespoons grilled lemon juice, capers, dill, parsley, diced shallot, Dijon mustard, salt, and pepper. Whisk until thoroughly combined. Refrigerate until ready to assemble.
06 - Place marinated barramundi fillets on the grill. Cook for 3-4 minutes per side until just cooked through and lightly charred. Fish should flake easily when tested with a fork. Internal temperature should reach 145°F.
07 - Place prepared cos lettuce leaves on the grill. Cook for 1-2 minutes per side until slightly wilted with nice grill marks and a subtle smoky flavor.
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 on both cut sides of each bun. Layer with grilled cos lettuce, barramundi fillet, tomato slices, and cucumber slices. Top with bun crowns.
10 - Serve immediately while fish is hot and lettuce retains slight crunch.