Place asparagus spears in a saucepan; mash with a fork. Pour in cream. Bring cream to a boil. Reduce heat and simmer, stirring occasionally, until thickened, about 20 minutes. Cover and keep warm.
Place chicken between 2 sheets of heavy plastic on a solid, level surface; firmly pound with the smooth side of a meat mallet to an even thickness. Season with salt and pepper.
Pour flour into a large, flat dish. Beat eggs thoroughly in a shallow bowl. Pour bread crumbs into another large, flat dish.
Dredge each piece of chicken in flour, dip in beaten eggs, and coat with bread crumbs.
Heat oil in a large skillet over medium-low heat. Cook breaded chicken in batches until golden brown and no longer pink in the center, about 5 minutes per side. Drain on a plate lined with paper towels. Serve with asparagus cream sauce.