01 - Fire up your BBQ or indoor grill to medium-high heat, approximately 400°F.
02 - Whisk together olive oil, lemon zest, minced garlic, sea salt, and black pepper in a shallow dish. Coat barramundi fillets thoroughly and let marinate for 10 minutes at room temperature.
03 - Lightly brush cos lettuce leaves with olive oil, coating both sides evenly.
04 - Place lemon halves cut-side down and jalapeño halves on the grill. Char for 3–4 minutes until softened and marked. Remove, let cool briefly, then finely mince jalapeños. Squeeze juice from grilled lemons.
05 - Combine mayonnaise, grilled minced jalapeños, 2 tbsp grilled lemon juice, capers, dill, parsley, diced shallot, and Dijon mustard in a bowl. Season with salt and pepper, mix thoroughly, and refrigerate until serving.
06 - Place marinated barramundi fillets on the grill. Cook for 3–4 minutes per side until fish flakes easily with a fork and shows light char marks.
07 - Place oiled cos lettuce leaves on the grill for 1–2 minutes per side until slightly wilted with smoky grill marks.
08 - Lightly toast burger buns on the grill, cut-side down, until golden and warm.
09 - Spread grilled lemon jalapeño tartare on both bun halves. Layer with grilled cos lettuce, barramundi fillet, tomato slices, and cucumber. Crown with top bun and serve immediately.