Combine lemon zest and juice, minced garlic, red pepper flakes, and chicken broth in a small bowl and set aside.
Slice each chicken breast in half horizontally to create 4 cutlets. Pat dry with paper towels and lightly season with salt and pepper.
Heat olive oil in a large skillet over medium heat. When the oil shimmers, carefully add chicken pieces and brown for 3 to 5 minutes per side. Chicken will not be fully cooked. Remove to a plate and keep warm.
To the same skillet, add shallots and cook until softened, about 2 minutes. Add chicken broth mixture and bring to a boil.
Return chicken to the skillet with any accumulated juices. Add asparagus pieces around chicken and sprinkle on minced basil. Bring to a boil, cover, and reduce heat to simmer until asparagus is tender, and chicken is no longer pink at the center and juices run clear, 10 to 15 minutes.
Remove cover and increase heat to medium. Melt butter, one tablespoon at a time, stirring continuously, allowing sauce to thicken a little. Remove from heat and stir in cream. To serve, place in a serving dish and garnish with additional fresh basil and lemon slices.