Melt 3 tablespoons butter in a large skillet; brown chicken in butter on all sides. Add water; cover, and cook over low heat 15 minutes or until chicken is tender. Set aside.
Melt remaining butter in a small saucepan; add onion, and sauté 2 minutes. Stir in flour, salt, and pepper. Gradually add half-and-half and wine; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in 2 tablespoons Parmesan cheese.
Arrange asparagus spears in 4 equal portions in a lightly greased 13- x 9- x 2-inch baking dish.
Place a chicken breast half on each portion of asparagus spears. Spoon sauce over chicken. Top with remaining cheese. Bake at 350° for 15 minutes or until lightly browned.