HEAT oven to 375°F.
MELT 1 tablespoon butter in medium skillet on medium high heat. Beat eggs with fork or whisk in medium bowl. Stir in cheese and pepper. Pour into skillet. Scramble eggs just until no longer runny. Remove from heat. Set aside.
PLACE flour in medium bowl. Cut in 6 tablespoons butter with pastry blender or 2 knives until crumbs are the size of small peas. Make a deep well in the center of flour mixture. Stir in buttermilk with a fork just until dough forms. If dry flour remains in bottom of bowl, add 1 more tablespoon buttermilk and stir. (All the flour may not be fully incorporated.)
TURN mixture onto lightly floured surface. Press dough into a ball. Knead 7 to 10 times. Press or roll dough into a rectangle, about 1/2-inch thick.
COAT baking sheet with no-stick cooking spray. Place dough on baking sheet. Roll out to a 12 x 10-inch rectangle. Gently lift sides of dough to loosen from pan. Spoon egg mixture lengthwise down center 1/3 of dough. Top with ham and green onions.
CUT diagonal slits in dough 1 inch apart on each side of filling. Lift strips of dough up and diagonally over the filling, alternating sides and overlapping ends of strips, creating a braid.
BAKE 22 to 25 minutes or just until light golden brown. Combine remaining 1 tablespoon butter, parsley and garlic salt in small bowl. Brush over warm braid. Cool on baking sheet on wire rack 10 minutes.