Cut kernels from 8 ears of corn, husks removed, and place in a large bowl.
Place cobs in a medium pot and add 2 Parmesan rinds (if using), reserved stems from 4 oz. shiitake mushrooms, 2 sprigs thyme, 1 bay leaf, 2 tsp. Diamond Crystal or 1 tsp. Morton’s kosher salt, and 8 cups water. Bring to a boil over high heat, then reduce to medium-low and simmer, stirring occasionally, until broth is fragrant and reduced by half, 40–50 minutes. Strain through a fine-mesh sieve into a medium bowl; discard solids and set broth aside.
Meanwhile, heat 4 Tbsp. unsalted butter in a large heavy soup pot or Dutch oven over medium-high. Add corn kernels, season generously with kosher salt and freshly ground black pepper, and cook, stirring occasionally, until corn is tender and juices have evaporated and browned on the bottom of the pot, 12–15 minutes. Reserve ½ cup corn for garnish; transfer remaining corn to a medium bowl.
Add ¼ cup dry white wine to pot and cook, scraping up browned bits, until liquid is syrupy, about 2 minutes. Scrape into bowl with remaining corn.
Melt remaining 1 Tbsp. unsalted butter in same pot over medium heat and cook 4 oz. thick-cut bacon, cut into ¼"; pieces, until golden brown and fat has rendered, about 6 minutes.
Add 1 lb. russet potatoes, peeled, cut into ½" pieces, 3 shallots, thinly sliced, 1 medium leek, white and pale green parts only, quartered lengthwise, thinly sliced, 2 garlic cloves, finely grated, and shiitake mushroom caps, cut into ¼" pieces, stirring occasionally, until vegetables have softened but haven’t taken on any color, 12–15 minutes.
Add 2 Fresno chiles, seeded, finely chopped and cook until fragrant and softened, about 3 minutes. Stir in 2 Tbsp. all-purpose flour and cook until nutty and fragrant, about 1 minute.
Add reserved broth, bring to a boil, and cook, stirring occasionally, until potatoes are fork-tender, 10–15 minutes.
Add 2 cups heavy cream and corn mixture and cook, stirring, until chowder has thickened, 5–10 minutes.
Remove from heat and stir in 1 Tbsp. chopped marjoram. Let sit 15 minutes before serving.Divide chowder among bowls. Top with chopped parsley or chives, oyster crackers, and reserved ½ cup corn; season with pepper.