Step 1

Cut kernels from cobs and place in a large bowl. Place cobs in a medium pot and add Parmesan rinds, if using, mushroom stems, thyme, bay leaf, 2 tsp. salt, and 8 cups water. Bring to a boil, then reduce heat 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.

Step 2

Meanwhile, heat 4 Tbsp. butter in a large heavy pot over medium-high. Add corn kernels, season generously with salt and 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 serving; transfer remaining corn to a medium bowl.

Step 3

Add wine to pot and cook, scraping up browned bits, until liquid is syrupy, about 2 minutes. Scrape into bowl with remaining corn.

Step 4

Heat remaining 1 Tbsp. butter in same pot over medium and cook bacon until golden brown and fat has rendered, about 6 minutes. Add potatoes, shallots, leek, garlic, and chopped mushrooms and cook, stirring occasionally, until vegetables have softened but haven’t taken on any color, 12–15 minutes. Add chiles and cook until fragrant and softened, about 3 minutes. Stir in 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 cream and corn mixture and cook, stirring, until chowder has thickened, 5–10 minutes. Remove from heat and stir in marjoram. Let sit 15 minutes before serving.

Step 5

Divide chowder among bowls. Top with parsley, oyster crackers, and reserved ½ cup corn; season with pepper.