Place one sheet of phyllo dough on a cutting board; brush with butter. Top with another sheet of phyllo; brush with butter. Repeat three times. Cut phyllo in half lengthwise, then cut widthwise into thirds. Repeat process so you have 12 stacks.
Grease 12 muffin cups. Sprinkle bread crumbs into bottom of muffin cups. Carefully place phyllo stacks into cups. Brush edges of dough with butter. Top each with cubes of cream cheese.
Break each egg separately into a custard cup; gently pour egg over cream cheese. Sprinkle with ham, provolone cheese and chives. Pinch corners of phyllo together to seal. Bake at 400°F for 13-17 minutes or until golden brown. Serve warm.