Combine water, sugar, and yeast in a large bowl; let stand 5 minutes. Lightly spoon flour into dry measuring cups; level with a knife. Add 1 cup flour and butter to yeast mixture; stir just until combined. Cover and let rise in a warm place (85°), free from drafts, 30 minutes.
Add pumpkin, salt, and nutmeg to flour mixture; stir until well combined. Add 2 1/4 cups flour and half of cheese; stir until a soft dough forms. Turn dough out onto a floured surface. Knead until smooth and elastic (about 8 minutes); add enough of remaining 1/4 cup flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel tacky).
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size. (Press two fingers into dough. If indentation remains, dough has risen enough.) Punch dough down; cover and let rest 5 minutes. Divide dough in half; shape each half into an 8-inch circle. Place dough circles on a baking sheet sprinkled with cornmeal. Sprinkle remaining cheese and nuts evenly over dough circles; press lightly to adhere. Lightly coat dough circles with cooking spray; cover and let rise 20 minutes (dough will not double in size).
Preheat oven to 400°.
Uncover dough; bake at 400° for 30 minutes or until loaves are browned on the bottom and cheese melts (shield loaves with foil to prevent overbrowning, if necessary). Cool on a wire rack.
Since I've made this recipe multiple times, I thought I'd add a review. I do think this bread is very nice and as one reviewer has said, it goes great with soup. My mother who doesn't generally like pumpkin likes this bread. For anyone who is new to making homemade bread, be prepared for sticky fingers. I've found using a scraper handy when the kneading the dough.
This was the best bread recipe I've ever made! I substituted 1 cup white whole wheat flour and added 3 1/2 tsp of vital wheat gluten. I used the bread hook on my mixer to knead the dough, and it turned out wonderfully.