In a large pot, pour about an inch of oil and heat to 375°F. Fry green beans in two to three batches for 1 minute each until wrinkly and tender, set aside on paper towels to absorb any excess oil.
In a large pan on medium heat, add a generous drizzle of oil along with the garlic and mushrooms. Sauté for about 7 minutes until the mushrooms have browned and are tender.
Add sake, mirin, miso, cream, and soy sauce and continue to simmer and stir for 2-3 minutes until the sauce has slightly reduced.
Turn off the heat, then add the fried green beans to the pan along with kosher salt and mix until combined.
Place into a serving bowl and top with sliced almonds and a drizzle of grated parmesan cheese to serve.
