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 for 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 for 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 and 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°F.
Uncover dough and 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.