Trent Pierce's Miso-Creamed Kale

INGREDIENTS

• 1 bunch lacinato kale, stems removed, roughly chopped (you should have 4 to 6 cups packed kale)
• 1/4 cup dry vermouth
• 2 cloves garlic, thinly sliced
• 1 large shallot, thinly sliced
• Salt and freshly ground black pepper
• 1/2 cup shimeji mushrooms with stems, or shiitake mushroom tops
• 1 tablespoon low-sodium soy sauce
• 3 to 4 tablespoons unsalted butter, divided
• 1 tablespoon white (shiro) miso, or more to taste
• 1/2 cup heavy cream