In a large bowl, dissolve yeast in warm water. Add the sugar, salt and 6 cups flour. Beat until smooth. Stir in enough remaining flour to form a soft dough.
Turn onto a floured surface, knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and refrigerate overnight.
Punch dough down; knead several times. Cover and let rest for 10 minutes. Meanwhile, in a small bowl, combine basil, walnuts and cheese; reserve 2 tablespoons for topping.
Shape dough into 32 balls. On a floured surface, roll each ball into a 4-in. circle; place 16 rolls each, seam side down, on two greased baking sheets with rolls touching. Cover and let rise until doubled, about 45 minutes.
Brush tops with butter; sprinkle with reserved basil mixture. Bake at 375° for 25 minutes or until lightly browned. Serve warm.