Over high heat, cook the spaghetti in a large pot of boiling salted water according to the package directions until al dente.
Meanwhile, heat the oil and butter in a 12-inch skillet over medium-high heat. Add the shallot and cook, stirring, until it just begins to color, 1 to 2 minutes. Add the mushrooms, 3/4 tsp. salt, and a few grinds of pepper and stir constantly until the mushrooms begin to release their liquid, about 3 minutes. Lower the heat to medium and cook, stirring occasionally, until soft and lightly browned, about 5 minutes more.
Add the port and stir to deglaze the pan. Add the cream and sour cream, bring to a simmer, and reduce the heat to medium-low. Cook, stirring frequently, until the liquid reduces to a saucy consistency, about 2 minutes.
When the spaghetti is al dente, reserve 1/2 cup of the cooking water and drain the spaghetti. Add the spaghetti and the reserved water to the sauce. Toss over low heat, sprinkle with the parsley or tarragon, and toss again to combine. If the sauce seems thin, continue to toss until it has thickened a bit. Season to taste with more salt and pepper. Serve, sprinkling with the parmigiano at the table.