Rinse the green asparagus and trim the tough ends. Peel the garlic and mince it finely. In a bowl, combine the basil pesto with the lemon zest and capers into a smooth sauce and set aside.
Heat a skillet over high heat with a splash of olive oil and simultaneously heat a grill pan or second skillet. Sear the salmon fillet in the first pan for exactly four minutes per side. In the other pan, toss the asparagus with a bit of olive oil and the minced garlic. Grill the asparagus for five minutes until tender-crisp.
Remove the seared salmon fillet from the pan and let it rest briefly. Toss the grilled asparagus once more through the warm garlic oil in the pan so the flavors distribute well.
Arrange the warm asparagus in the center of a plate. Place the seared salmon fillet directly on top and spoon the cold sauce of pesto, lemon zest and capers over the fish and vegetables.