How to quickly cook fresh asparagus in a skillet with plenty of garlic – and if you like, a little anchovy! But if you're not into anchovies, no problem: anchovies or not, a quick sauté is a basic, even essential, method for cooking asparagus. This bright-green asparagus is simple but sumptuous, definitely worth the best asparagus you can find but also a reliable way to turn supermarket asparagus into something quite remarkable.