Clean your asparagus and use a carrot peeler gently to remove the thick skin along the bottom. The result should not be white but a paler green from below the head down. Trim the ends off. Cut in pieces as in the picture.
Heat olive oil in non stick pan (about 2 tsp) at medium heat. Add asparagus and cook until bright. Meanwhile, boil the pasta until al dente (very important not to overcook for this one). When done, drain and add to asparagus, turning to low. Add the pesto, mix, and turn off heat immediately. Serve by itself or with some meat or other dish.
By the way, troffiette is a Ligurian specialty (as is Pesto aka “pesto genovese,” I’ve mentioned before basil grows like weeds in the seaside, Italian riviera hillside that is Liguria, let’s not even start to talk about the ligurian foccacia, lobster-like delicious seafood, or wines on this tangent), though it’s not impossible to find in the US or to make yourself. It’s a very easy to make shape, the hardest part is cutting the peice of pasta dough you’re going to work with small enough and using a fine enough ground wheat flour in its construction, as well as letting it rest long enough to cooperate with you. But I encourage you to try to find it or make it.