Melt the butter in a wide sauce pot over medium-high heat. Add the shallots and saute until tender and aromatic, about 2 minutes. Stir in the mushrooms and cook 4-5 minutes more, until the mushrooms are tender and any liquid has evaporated. Stir in the soy sauce and cook until dry.
Sprinkle the flour over the mixture in the pot and stir thoroughly to incorporate. Cook the mixture 1 minute, stirring constantly until the very thick. Stir in the chicken stock 1 cup at a time, stirring thoroughly between each addition to make sure the liquid is completely smooth. Add the thyme and bring the pot to a simmer. Cook at a simmer 5 minutes, then remove from the heat and discard the thyme stems. Stir in the cream cheese and reserve warm.
Place a large sauté pan over high heat, add half of the olive oil and 2 cloves of garlic. When the garlic is sizzling and browned, stir in ½ of the red chili and immediately add half of the kale and ½ teaspoon kosher salt. Sauté quickly for 2 minutes, stirring constantly with tongs. Transfer the cooked kale to pot with the chicken stock and mushroom veloute. Wipe out the pan with a paper towel and repeat with the remaining oil, garlic, chili and kale.
Stir together all of the cooked kale with the mushroom veloute and mix well. Season to taste with salt.
Transfer the kale to a 2 qt gratin or 13 x 9 baking dish. At this point the dish may be held at room temperature for up to 2 hours before serving or covered and refrigerated for up to 48 hours.
To serve, preheat the oven to broil. Scatter the parmesan and almonds over the top of the gratin. Place the dish on a low rack below the broiler until the cheese and almonds are golden brown. If the kale is not hot all the way through, turn the oven to bake at 375°F and continue cooking until hot. If the top of the dish begins to darken too much, cover with aluminum foil while heating.