Fill a large stock pot 3/4 the way with water. Season with kosher salt according to the pasta directions (typically 1-2 tbsp) and bring it to a boil over high heat.
In the meantime, cook the mushrooms. Heat a large skillet over medium high heat. Season with olive oil. Once the oil is shimmering, add the shiitake and maitake mushrooms in a single layer onto the pan. Season with a pinch of kosher salt. Let them cook undisturbed, about 3 minutes, until golden brown on one side. Flip, then reduce the heat to medium. Let the other side cook for 5-7 minutes, until golden brown. Keep an eye on them to prevent burning. Remove them from the pan once they are a deep golden brown.
If using king trumpet mushrooms, season the pan with a little more olive oil and adjust the heat back to medium high. Place the king trumpet mushrooms into the pan in a single layer and season with a pinch of salt. Sear, undisturbed, for 3-5 minutes until golden brown. Flip, then sear until golden brown on the other side. Remove from the pan and turn off the heat. Leave all of the golden brown bits in the pan!
Return to the boiling stock pot of water. Cook the pasta until al dente (according to box instructions,) or 1-2 minutes before al dente if you like your pasta on the firmer side.
Once the pasta is done, remove 1/3 cup of pasta water from the stock pot and use it to deglaze the golden brown bits off of the skillet. Add the corn purée to the skillet with the pasta water and stir with a rubber spatula or spoon until a sauce is combined. Transfer the pasta over to the sauce and toss until fully coated. Grate Parmesan cheese on top then toss the pasta again.
Plate the pasta and top with mushrooms and chopped chives. Enjoy!