Heat a tablespoon of butter and a tablespoon of olive oil in a large pan. Wait until the pan is hot and the butter has fully melted. Add the salmon and asparagus, season with salt and pepper , and cook for about 3-4 minutes on one side.
Flip and cook for about 3-4 minutes on the other side. Add the garlic and lemon zest. Cook the garlic for just 1-2 minutes or until it begins to brown. Turn off the heat and squeeze half a lemon into the dish.