1. Preheat oven to 425°. Combine flour and cornmeal in a large bowl. Cut butter into 1/2-inch-thick slices. Sprinkle butter over flour mixture, and toss. Cut butter into flour mixture with a pastry blender until crumbly. Cover and chill 10 minutes. Stir in chives. Add buttermilk, stirring just until dry ingredients are moistened.
2. Turn dough out onto floured surface, and knead 3 or 4 times, gradually adding additional self-rising flour as needed. With floured hands, pat dough into a 3/4-inch-thick rectangle (about 9 x 5 inches); dust top with flour. Fold dough over itself in 3 sections, starting with short end (as if folding a letter-size piece of paper). Repeat 2 more times, beginning with patting dough into a rectangle.
3. Pat dough to 1/2-inch thickness. Cut with a 2-inch round cutter, and place, side by side, on a parchment paper-lined or lightly greased jelly-roll pan. (Dough rounds should touch.)
4. Bake at 425° for 13 to 15 minutes or until lightly browned. Remove from oven; brush with 2 Tbsp. melted butter.
Note: We tested with White Lily soft-wheat self-rising flour.