Add pasta to a large pot of boiling salted water and cook until al dente. Drain in a colander and let cool.
Meanwhile, slice asparagus on the bias into 1/2-inch pieces. Place the asparagus on a sheet tray and drizzle with olive oil, and season with salt and pepper. Place in oven and roast for 10 minutes, until slightly tender. Remove and let cool.
In a small bowl, combine shallot, garlic, mustard, lemon zest, lemon juice, and red pepper flakes. Whisk in olive oil and season with salt and pepper. Add chives.
Add pasta and roasted asparagus to a large bowl. Drizzle with dressing and toss. Add the crumbled feta cheese, toss and serve.