Steam the asparagus for 2-3 minutes. Heat 3 tbsp of the oil in a non-sticking frying pan over medium high heat, add the asparagus, season with salt and pepper, and then sauté for a couple of minutes.
Remove the cooked asparagus onto a plate. Add 2 tbsp of the oil to the pan, add the chicken stripes, season with salt and pepper and cook until thoroughly cooked, about 4-5 minutes. Put the asparagus back to the pan.
In the meantime, cook the Tortelloni according to package instructions and drain, reserving a ladleful of the pasta cooking water. Add the pasta to the pan and stir gently, adding some of the pasta water if you need to loosen the sauce. Season to taste.
Divide among 2 plates, drizzle with little oil, sprinkle with Pecorino Romano shavings and serve.