Cook pasta in boiling water 10 minutes or until al dente; add asparagus during final 2 minutes of cooking. Drain pasta mixture in a colander over a bowl, reserving 1/3 cup cooking liquid. Combine reserved cooking liquid, eggs, and milk, stirring with a whisk.
Heat a large nonstick skillet over medium-high heat. Add oil and onion to pan; sauté 2 minutes. Add pasta mixture; stir to combine. Remove from heat; stir in milk mixture, chicken, and cheese. Place pan over medium heat, and cook 4 minutes or until slightly thick, stirring frequently. Remove from heat; stir in parsley, salt, pepper, and bacon. Serve immediately.