Combine 1 cup flour, sugar, chives, basil, garlic salt and yeast in the bowl of an electric mixer; mix well.
Combine milk and butter in small saucepan; heat until very warm, 120 to 130°F. Add warm liquid and egg to flour mixture; mix on low speed until blended. Beat on medium speed for 2 minutes. Stir in an additional 1 to 1 1/2 cups flour by hand until dough pulls away from side of bowl.
Turn dough out onto lightly floured surface. Knead dough for 5 minutes or until smooth and elastic. Place dough in greased bowl; turn to grease top. Cover and let rise in warm place until doubled in size, 50 to 60 minutes.
Lightly grease 12 medium muffin cups. Divide dough into 12 equal pieces. Shape each into a ball, pulling dough under to make a smooth top. Place 1 ball, smooth side up, in each prepared muffin cup. Using kitchen shears, cut balls of dough into quarters almost to bottom. Brush lightly with melted butter.
Cover; let rise until doubled in size, 25 to 30 minutes.
Preheat oven to 375°F. Bake rolls 15 to 20 minutes or until golden brown.
Makes 12 rolls.