Put the dried porcini mushrooms in a bowl and cover with 1.5 cups very hot water; soak 20 minutes, then lift out, squeeze dry, chop, and strain the soaking liquid through a paper towel–lined sieve; reserve 1 cup.
Bring a large pot of water to a rolling boil.
Warm the extra-virgin olive oil and half of the unsalted butter in a wide skillet over medium heat until the butter foams.
Add the shallot and cook, stirring, until translucent, 2–3 minutes; add the garlic and cook until fragrant, 30–60 seconds.
Pour in the dry white wine; simmer until almost evaporated, 1–2 minutes, then add 3/4 cup of the reserved soaking liquid and cook until reduced by about half, 5–7 minutes.
Salt the boiling water with the kosher salt, add the tagliatelle, and cook until al dente (2–3 minutes for fresh, 8–10 minutes for dried), reserving some pasta water.
Transfer the pasta to the skillet along with a splash of pasta water; add the remaining butter and toss vigorously over medium heat until the sauce emulsifies and coats the noodles, 1–2 minutes, loosening with more soaking liquid as needed.
Stir in the flat-leaf parsley and season with the black pepper; taste and adjust with pasta water if needed.
Serve immediately with Parmigiano Reggiano cheese, finely grated (for serving).