Blend water, yeast and sugar in a large mixing bowl. Let stand, undisturbed, for about 5 minutes, or until it start to foam and bubble.
Stir melted butter (or oil) and one cup of the flour into the yeast mixture to blend. Cover with a damp cloth and let rise in a warm place (but not the oven) for about 30 minutes.
Add pumpkin puree and salt to mixture and stir to combine. Add 1/3 cup of Gruyere and 2 cups of the flour and combine until you have a soft dough. Turn the dough out onto a floured cloth or board and knead until smooth and elastic, about 5 minutes, adding enough of the remaining flour as needed to keep the dough from sticking to the board or your hands. The dough should be soft.
Place the dough into a greased bowl (we use cooking spray) and turn once to coat the top and bottom. Cover with the damp cloth and allow to rise again in a warm place until doubled in size, about 1 hour.
While dough is rising, begin to caramelized the onions by placing sliced onions in a pan with 2 tbsp. of olive oil and cook over low heat until soft and beginning turn golden brown. Add a little bit of water at a time to keep the onions from drying out. Once caramelized, set aside until ready to assemble the bread rounds.
Once dough has doubled in volume, poke your finger into the dough and if the indentation remains, the dough is ready to shape.
Line a large baking sheet with parchment paper and sprinkle cornmeal evenly on top of the parchment. Preheat oven to 400℉.
Punch dough down and divide in two. Shape each half into a circle about 7-9 inches in diameter. Place on the prepared baking sheet.
Brush the tops of the dough with olive oil and arrange caramelized onions and walnuts on top. Sprinkle remaining Gruyere on top of everything. Gently press all of the toppings in toward the dough. Let rise for 20 minutes
Bake for 25 minutes, or until loaves are golden brown and cheese is melted.