Cut butter into flour with a pastry blender until crumbly; add Parmesan cheese and chives. Add buttermilk, stirring until dry ingredients are moistened.
Turn dough out onto a lightly floured surface; knead 3 or 4 times. Pat or roll dough to 3/4-inch thickness; cut with a 3-inch round cutter, and place on a lightly greased baking sheet. Bake at 425º for 12 minutes or until golden. Set biscuits aside, and keep warm.
Combine wine and green onions in a large nonstick skillet; bring to a boil. Reduce heat to medium, and cook 6 minutes or until wine is reduced by half. Add spreadable cheese; reduce heat, and whisk until cheese melts. Stir in Alfredo sauce. Add crawfish meat with liquid and Creole seasoning; cook over medium-low heat until thoroughly heated.
Split warm biscuits in half horizontally. Spoon half of crawfish mixture evenly over bottom biscuit halves; top with remaining biscuit halves. Spoon remaining crawfish mixture evenly over the top of each biscuit. Garnish, if desired.