01 - Heat your BBQ grill or indoor grill pan to medium-high temperature.
02 - Whisk together olive oil, lemon zest, minced garlic, sea salt, and black pepper in a shallow dish. Add barramundi fillets and turn to coat evenly. Let marinate for 10 minutes.
03 - Lightly brush cos lettuce leaves with olive oil on both sides.
04 - Place lemon halves cut-side down and jalapeño halves on the preheated grill. Cook for 3 to 4 minutes until charred and softened. Remove and let cool slightly. Finely chop the grilled jalapeños and squeeze juice from the grilled lemons.
05 - Combine mayonnaise, chopped grilled jalapeños, 2 tbsp grilled lemon juice, capers, dill, parsley, diced shallot, Dijon mustard, salt, and pepper in a bowl. Mix thoroughly. Refrigerate until ready to assemble.
06 - Place marinated barramundi fillets on the grill. Cook for 3 to 4 minutes per side until just cooked through and lightly charred. The fish should flake easily when tested with a fork.
07 - Grill brushed cos lettuce leaves for 1 to 2 minutes per side until slightly wilted with smoky grill marks.
08 - Lightly toast the cut sides of burger buns on the grill for about 30 seconds to 1 minute until golden.
09 - Spread grilled lemon jalapeño tartare generously on both cut sides of each bun. Layer with grilled cos lettuce, followed by a barramundi fillet, then tomato slices and cucumber slices if using. Top with the bun crown.
10 - Serve burgers right away while fish is hot and lettuce retains its slight crunch. Pairs excellently with Australian Sauvignon Blanc or a crisp pale ale.