Combine 1 cup flour, oats, sugar, undissolved yeast and salt in large mixer bowl. Heat water and butter until very warm (120° to 130°F). Gradually add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Stir in walnuts and enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes.
Roll dough to 12 x 8-inch rectangle. Beginning at short end, roll up tightly as for jelly roll. Pinch seam and ends to seal. Place, seam side down, in greased 9 x 5-inch loaf pan. Cover; let rise in warm, draft-free place until doubled in size, about 1 hour.
Bake at 375°F for 35 to 40 minutes or until done. Remove from pan; cool on wire rack. Brush melted butter on top.
* To toast oats: Spread oats in thin layer in shallow baking pan. Bake at 350°F for 10 to 12 minutes or until light golden brown, stirring often.