Bring a large pot of salted water to a boil. Cook the tagliatelle pasta according to package instructions until al dente. Reserve 1 cup of pasta water before draining.
In a large skillet, heat the olive oil over medium heat. Add the sliced truffles and cook for 2-3 minutes, until fragrant.
Add the butter, garlic, salt, and pepper to the skillet. Cook for an additional 2 minutes, until the butter is melted and fragrant.
Add the white wine to the skillet and cook for 2-3 minutes, until reduced by half.
Stir in the heavy cream and bring the mixture to a simmer.
Add the cooked tagliatelle pasta to the skillet, tossing to coat with the truffle sauce.
If the sauce seems too thick, add some reserved pasta water.
Remove the skillet from the heat and stir in the Parmesan cheese until melted.
Serve immediately, garnished with chopped parsley and additional truffle slices if desired.