Cook chicken in a lightly greased nonstick skillet over medium-high heat 7 to 8 minutes on each side or until lightly browned. Remove from skillet; chop chicken, and set aside.
Melt 2 tablespoons butter in nonstick skillet over medium heat; add shallots and onion, and sauté 3 minutes. Add mushrooms, and sauté 5 minutes. Reduce heat to low; add cream cheese and milk, stirring until blended.
Remove from heat; add chopped chicken. Stir in sherry and next 3 ingredients.
Unfold 3 pastry sheets on a lightly floured surface; cut into fourths. Roll into 10-inch squares.
Place 1 cheese slice and 1 ham slice on center of each puff pastry square; top with 1/4 cup chicken mixture. Bring corners together over filling, gently pressing to seal.
Cut remaining pastry sheet into thin strips; tie each bundle with pastry ribbon. Place on a baking sheet; brush with egg white.
Bake at 400° for 35 minutes or until golden. Whisk together melted butter and next 3 ingredients. Serve over pastry bundles.