For the Rhubarb Compote:
Remove the tough ends of the rhubarb and reserve for the Tagliatelle. Cut the rhubarb ribs into thick slices. Combine the rhubarb, sugar, and water in a pot and bring to a boil. Turn down the heat to low and cook for 15 to 20 minutes. Remove from the heat and refrigerate.
For the Tagliatelle:
Combine the olive oil and reserved rhubarb scraps in a double boiler; infuse the mixture on low heat for 20 minutes. Remove from the heat, and cool the oil to room temperature. In a separate bowl, combine the flour and salt. Once combined, form a well in the center of the flour and slowly incorporate the eggs and oil into the flour mixture. Knead the pasta dough for 10 minutes on a floured work surface, wrap in plastic wrap, and refrigerate for 4 hours. Roll the dough as thinly as possible with a rolling pin, and slice the pasta to your desired thickness.
For the Rhubarb Demi-Glace:
In a small pot, combine the pork demi-glace with 2 tablespoons of the Rhubarb Compote; cook for 5 minutes to combine the flavors. Whisk in the butter to give great flavor and a glossy look.
To Assemble and Serve:
Bring a large pot of salted water to a boil, add the Tagliatelle to the pot, and cook for 2 to 3 minutes. Drain the pasta and combine with the Rhubarb Demi-Glace in a sauté pan on medium heat, tossing to coat the pasta with the sauce. Twirl the pasta with a carving fork and plate. Put the egg yolk in the center of the pasta, and sprinkle with chives.