Fill the bottom pot of your steamer with a couple inches of hot water. Set it on the stove, covered, over high heat to bring it to a boil.
While the water is heating, rinse your asparagus and cut off the bottom two inches. Add the asparagus to your steamer basket.
When the water is boiling, place the steamer basket on top of the boiling pot and cover the steamer basket with a lid. Steam your asparagus for 10 minutes, or until it is just tender.
When the asparagus is almost done cooking, place your butter in a small, microwave-safe bowl and cover it with wax paper. Melt the butter in the microwave. Rub the tarragon between your thumb and fingers to crush it up a bit, and sprinkle it into the melted butter. Add your pepper and stir to blend.
Serve the asparagus in a platter with the bowl of tarragon butter on the side. Each person can spoon some tarragon butter over his or her portion. Store leftovers in the refrigerator for up to four days.
If you don't have a steamer, you can add an inch of hot water to a large skillet and bring it to a boil. Add the asparagus to the pan and cook until it is just tender.