Preheat a stovetop smoker until very hot and toss in a handful of soaked hickory chips. In a large bowl stir to combine mushrooms with 3 tablespoons oil and 1 tablespoon Creole seasoning, or to taste. When the smoker begins to smoke, add the mushrooms and stir with a long pair of tongs to evenly distribute. Cook until smoky flavor penetrates the mushrooms, about 20 to 25 minutes. Transfer mushrooms onto a baking sheet to cool.

Heat remaining 1 tablespoon oil in a sauté pan, add Tasso and sauté, shaking pan frequently, 2 minutes. Add shallots, green onions and smoked mushrooms, and cook, tossing 2 minutes. Add garlic and cream, bring to a boil, reduce heat and simmer to reduce slightly. Add the butter to the sauce, taste, and adjust the seasoning with Creole seasoning and/or salt if necessary. Add the pasta to the sauté pan and cook, tossing the pasta with the sauce until thoroughly coated and warmed through. Divide the pasta between 4 warmed plates. Garnish with green onions and Parmesan.