For the soup, place a large pot over medium-high heat with enough oil to coat the bottom of the pan. Add the squash, potatoes, onion, apple, fennel and garlic to the pot, and season with salt. Stir to coat the mixture with the oil and sweat veggies 5-6 minutes. Add the wine to deglaze the pan and cook until reduced by half. Add the vegetable stock and season with salt and red pepper flakes. Bring to a boil, reduce to a simmer and cook until the squash is falling apart, 35-40 minutes. Add water if necessary to keep the squash submerged.
Purée the soup with a handheld immersion blender. (If using a countertop blender, cool the mixture for about 5 minutes before carefully adding it to the blender.) Blend until very smooth and velvety. If it is too thick, add water to thin. Season to taste, adding the sugar if needed.
Whip the cream in a large bowl until it holds its shape in soft peaks. Refrigerate until ready to use.
For the Oyster Mushroom Chips, preheat oven to 375°F.
Put the mushrooms in a large bowl and toss with olive oil until lightly coated; season with salt and red pepper. Using two baking sheets, spread the mushrooms out in a single layer—you don’t want them to overlap.
Roast the mushrooms for 10-12 minutes or until brown and "cooked on"/stuck to the baking sheets. Remove from the oven and let cool for 5 minutes. Using a bench scrape, scrape the mushroom chips off the bottom of the baking sheet and chop.
For the Grilled Cheese Soldiers, spread 1 tablespoon of mayo on one side of each slice of bread. With the mayo side facing down, place 1/2 of the grated cheddar on one slice of bread, covering the entire surface out to the corners. Place apple slices in a row across the cheese then top the apple slices with the bacon. Sprinkle the remaining grated cheddar on top of bacon, covering it evenly, and place the second bread slice on top with the mayo side facing up.
Heat a nonstick skillet over medium heat. Place sandwich in the pan, cook 3 minutes or until brown and crispy then flip and repeat on other side. Remove from pan and cut sandwich into planks.
To serve, ladle the soup into bowls and top each with a dollop of the whipped cream and some chopped Oyster Mushroom Chips. Garnish with minced chives. Serve with the grilled cheese soldiers alongside.