Cook the tagliatelle
Cook the tagliatelle in salted boiling water. Cook until al dente, according to package instructions.
Crush the garlic cloves to release the flavor. In a skillet, melt the butter over medium heat. Add the olive oil, 1/4 tsp ground black pepper, and the crushed garlic. Cook for about 30 seconds. Add about 1 tablespoon of freshly grated black truffle (about half of the truffle) and cook for another 30 seconds. Pour the stock (or water) into the skillet and stir well to combine. Remove the garlic cloves
Drain your tagliatelle (reserve about 50 ml of the cooking water). Add the tagliatelle to the sauce and toss to combine. Remove from the heat and grate the parmesan over the pasta. If necessary add the reserved pasta water to get a nice silky sauce. Grate the remaining fresh truffle over the pasta, then serve.