Heat the oil with the garlic over low heat without burning the garlic. Add the artichokes and saute a few minutes, stirring.
Add the wine and bring to a boil, reduce heat and simmer 20 minutes or until artichokes are soft. Add a little water if necessary. Add dill and salt and pepper to taste and remove from heat.
Cook the tagliatelle until al dente. In a mixing bowl, combine the mascarpone with half a ladle of the pasta cooking water until smooth.
Drain the pasta and add to the bowl with the mascarpone. Add the artichokes and stir well. Serve and top with Parmesan cheese.