Prepare the Dough:

1. In a large bowl, combine milk, honey and yeast, stirring until the yeast dissolves. Set aside to proof for 5 minutes, or until the mixture is slightly foamy.
2. Add 1 cup of flour into the yeast mixture, and stir until just barely combined. Cover with a clean dishcloth and place in a warm draft-free place to rise for 30 minutes.
3. After half an hour, stir in the pumpkin, sage, olive oil, salt and pepper. Add the shredded cheese and remaining 2 1/2 cups flour, and mix until the dough comes together into a ball.
4. Transfer the dough to a clean, lightly floured work surface, and knead until soft and elastic, about 8 minutes, adding flour as needed to keep the dough from sticking (don't go nuts with the flour, though - the dough should still feel very soft and slightly tacky). Shape into a ball.
5. Place the dough in a lightly-oil bowl, turning over to coat the top. Cover with a clean dishtowel, and let rise in a warm draft-free place for about an hour, or until doubled in size.

Prepare the Topping:

1. Meanwhile, prepare the caramelized onion topping.
2. Melt the butter and oil in a large heavy-bottomed skillet set over medium-high heat. Add the onion, and cook about 5-7 minutes or until softened and beginning to brown. Reduce the heat to medium, and stir in the balsamic and honey. Continue cooking, stirring occasionally, until onions are very soft and caramelized, about 10 minutes. Season to taste with salt and pepper. Set aside to cool.

Shape and Bake the Dough:

1. When the dough has doubled in size, punch down, then cover again and let rest for 5 minutes. Divide into halves, shaping each half into a ball, then flattening out into an 8" circle about 1" thick.
2. Place each loaf onto a parchment-covered baking sheet. Cover and let rise for another 20 minutes, or until almost doubled again in size.
3. Preheat oven to 425F. Using your fingers, make several dimples into the top of each loaf. Brush with a little olive oil, then spoon the onion mixture onto the tops of the loaves. Finish with a sprinkling of coarsely chopped fresh sage, if desired.
4. Bake in preheated oven for 20-25 minutes, or until puffed and golden brown. Serve immediately, or cool to room temperature on a wire rack.