Add water enough to cover the veggies and the chicken breast or carcass. Bring to a rapid boil stirring enough to prevent sticking on the bottom of the pot.
As that boils the, squash should be finished up. Spoon the good stuff out of the squash into a bowl. It should be soft enough to do this easily. Scrape as much from the peel as you can. Feel free to taste some as you do this. Poor the left over water from the squash pans into the soup pot. After all the squash is spooned away from the skins put it in the soup pot. Once again, add enough water to just cover everything. If you used a chicken carcass now is the time to remove it and debone it. This is also the time to add the diced Heirloom Tomato. You can remove the skin of it if you want, but not necessary.
Keep this at a medium boil for about 45 minutes. This time allows the flavors to meld and gives you time to clean up your mess in the kitchen so far. Once the mess is cleaned up lower the heat to low and add the cheese. It is best if you break it into small pieces or shred it. Keep stirring until all the cheese is melted and slowly add half of the milk while stirring. The milk smooths out the texture and lightens the color.
Now that all the ingredients are together use some sort of hand or wand mixer to emulsify the soup. This blends it all together and makes a nice smooth texture. This is also when I like to taste it and add the rest of the seasonings to taste. I find a little more salt and sage gives it a nice pop at the end. The longer you blend the smoother it gets. At this point you will want to remove it from the heat.
Portion into bowls or cups and top with a dollop of Creme Fraiche, the fresh sage and crisped shallots. To achevee the crisped shallots, slice it very thin and saute over medium heat with butter until browned. Enjoy!