For the pasta: Sift together the flour, cocoa and sugar. Add a pinch salt and mound the flour mixture in a large bowl or on a clean work surface. Hollow out the center, making a well in the middle of the flour with steep sides. Break the eggs into the well. Add the chocolate syrup and vanilla. Gently mix together with a fork. Gradually start incorporating the flour by pulling in the flour from the sides of the well. As you incorporate more of the flour, the dough will start to take shape. Once it gets thick, you can use a spatula to incorporate the rest of the flour.
If the dough is too dry, add a little water. If the dough is too wet or sticky, add a little flour. Once the dough comes together, knead the dough on a clean work surface until it becomes smooth, about 8 minutes. Shape into a disc, cover with plastic wrap and let rest in the fridge, 20 to 30 minutes.
Divide your rested dough into quarters and work with one piece at a time, covering your other pieces to keep them moist. Flour each piece lightly, shape it into a rectangular shape and put it through a pasta sheeter attachment, starting at the widest setting. Run the dough once through the largest setting, fold it into thirds and run it through one more time. Then run the pasta through the sheeting attachment once on every number, stopping at 5 or 6, depending on how thick you would like it. Lightly flour the rolled out pasta sheet and fold in half. Take your chef knife and cut ribbons about a 1/2-inch thick, then unravel the pasta ribbons and place on a floured baking sheet to keep from sticking.
For the sauce: Bring the heavy cream to a simmer in a heavy-bottomed saucepan over medium-high heat and stir in the chocolate-hazelnut spread. Add a pinch salt and continue whisking until the sauce is creamy. Remove from the heat and reserve.
Cook the chocolate pasta in a large pot of boiling water, 3 minutes. Immediately remove the pasta from the water and toss gently with the sauce and a little of the pasta cooking water to help with the consistency.
Mound the pasta and sauce on dessert plates and garnish with the fresh berries, a dollop of creme fraiche, white chocolate shavings and skinless toasted chopped hazelnuts, to garnish.