Heat the oil in a deep saute pan. Add the salmon fillets, skin-side down, and the asparagus. Fry gently over a low–medium heat until the salmon is crispy and the asparagus is slightly charred.
Turn the fish over, add the garlic and cook for 1 minute, then add the cherry tomatoes and a little splash of water and cook for 4 to 5 minutes until the tomatoes have started to break down. Add plenty of seasoning and a squeeze of lemon juice. Scatter over the basil leaves and serve.