Fill a large stockpot with 3 quarts water, and bring to a boil.
While waiting for the water to boil, pour the cream into a skillet with the lemon and orange zest. Cook over medium heat, stirring frequently with a wooden spoon, until the cream lightly coats the sides of pan, 2 to 4 minutes after it comes to a boil.
Add the cognac (if using) and the mint leaves, and cook another 2 minutes. Season with salt and set aside.
When the water comes to a boil, add the kosher salt, and cook the tagliatelle until al dente. Lightly drain, and then transfer to the cream mixture, and cook for 1 minute, moving everything around with tongs to combine the ingredients. Add the Parmigiano-Reggiano, stir well, and serve.