Peel and coarsely grate the beetroot, finely dice the shallot.
Heat the oil and sauté the shallot until translucent, add the beetroot and sauté. Pour in the vegetable stock and bring to the boil. Season everything with vinegar, salt and pepper. Cover the vegetables and cook them al dente over a low heat for about 25 minutes.
In the meantime, cook the pasta in salted water.
Mix the beetroot vegetables with the crème fraîche. Mix the tagliatelle and vegetables carefully.