Follow the steps in order for the best result.
Place a large skillet on the stove and heat over high heat until very hot.
Add the asparagus to the hot skillet and cook for approximately 1 minute, allowing it to begin to sear.
Reduce the heat to medium.
Add the butter to the skillet.
Continue cooking, stirring frequently, until the butter melts and begins to brown slightly, about 1 minute.
In a small bowl, whisk together the Dijon mustard, lemon juice, and black pepper.
Pour the mustard mixture into the skillet with the asparagus and butter.
Cook, stirring occasionally, until the asparagus is tender-crisp, about 5 to 7 minutes. Be careful not to overcook the asparagus; it should still have a slight bite.