In bowl, mash together feta cheese, egg yolks and garlic. Mix in onions, parsley, mint and pepper.
Cut chicken breast in half almost but not all the way through; open like book. Spread feta mixture evenly on 1 half of each breast; fold breast over to enclose.
Place 1 sheet of phyllo on work surface, keeping remainder covered with damp towel to prevent drying out. Brush lightly with some of the butter; top with second sheet and brush lightly with butter. Centre 1 breast on phyllo about 2 inches (5 cm) from short edge; fold long sides over chicken and roll up. Repeat with remaining chicken.
Place in lightly greased baking dish; brush with remaining butter. (Make-ahead: Cover and refrigerate for up to 8 hours.).
Bake in 350°F (180°C) oven until crisp and golden, about 45 minutes. Serve with lemon wedges.