Preheat oven to 400°.
Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add mushrooms and shallot; cook 6 minutes. Add spinach and parsley; cook 1 minute. Transfer to a bowl. Stir in breadcrumbs, egg white, 1/4 teaspoon salt, and 1/4 teaspoon pepper.
Sprinkle chicken with 1/4 teaspoon each salt and pepper. Arrange chicken breasts between 2 sheets of heavy-duty plastic wrap; flatten to 1/4-inch thickness using a meat mallet.
Spoon mushroom mixture onto center of chicken breasts. Roll up and secure with wooden picks. Dredge chicken breasts in flour, shaking off excess.
Wipe pan clean with paper towels. Heat 2 teaspoons oil in pan over medium-high heat; add chicken. Cook 5 minutes, turning frequently, until browned. Transfer chicken to a baking sheet lined with foil. Bake at 400° for 13 minutes or until done.
Add wine to pan; cook 2 minutes over medium heat, scraping pan to loosen browned bits.
Whisk together cream sauce mix, broth, and milk; add to pan. Bring to a boil; reduce heat, and simmer 1 minute. Stir in lemon juice.
Remove wooden picks from chicken; cut into 1-inch-thick slices. Spoon sauce onto serving plates; arrange chicken over sauce.