For the pasta dough: Combine the flour, eggs and yolk in a food processor and pulse until a dough comes together. Transfer to a counter dusted lightly with flour and knead gently until the dough comes together and is smooth, about 1 minute. Wrap in plastic and refrigerate for at least 30 minutes and up to 24 hours.
Divide the dough into 4 pieces. With your hands, flatten and shape one piece of dough into a 1/2-inch-thick rectangle. Dust it lightly with flour and pass it through the widest setting on the pasta machine. If the dough comes out oddly shaped, reform into a rectangle. Fold it in thirds, like a letter, and if necessary, flatten it to a 1/2-inch thickness. Pass it through the widest setting again with the seam of the letter perpendicular to the rollers. Repeat this folding and rolling step 10 to 12 times, dusting the dough with flour if it becomes sticky.
Without folding the dough, pass it through the next setting on the pasta machine. Keep reducing the space between the rollers after each pass, lightly dusting the pasta with flour on both sides each time, until the pasta is about 1/16-inch thick and 3 inches wide.
Lay the rolled-out dough on a counter. Roll out the remaining dough in the same manner. Cut each strip of dough into 11-inch lengths. Cut the dough into fettuccine. (Alternatively, use store-bought dried or fresh fettuccine.)
For the meat: Heat the oil in a large saute pan over medium heat. Add the bacon and cook slowly until the fat is rendered and the bacon is crisp, 8 to 10 minutes. Transfer the bacon with a slotted spoon to a plate lined with paper towels.
Increase the heat to high, add the chuck and pork to the pan and season with the fennel, chile flakes, salt and pepper. Cook, stirring occasionally, until golden brown, about 10 minutes. Drain the excess fat from the pan.
For the quick bolognese sauce: Heat the oil in a large Dutch oven over medium-high heat until it begins to shimmer. Add the celery, fennel, onion and carrot and cook until soft, about 5 minutes. Add the garlic and cook for 1 minute. Add the tomato paste and ground fennel and cook for 1 minute more.
Add the wine and cook until reduced by half, about 3 minutes. Add the tomatoes and chicken stock and cook until the tomatoes begin to soften, about 10 minutes. Coarsely mash the tomatoes using a potato masher or wooden spoon, season with salt and pepper and cook until the sauce comes to a boil and begins to thicken slightly, about 15 minutes. Add the cooked bacon, chuck and pork to the pan and continue cooking until the sauce is thick, about 15 minutes more. Fold in the parsley and oregano and season with salt and pepper.
For the garlic bread: Preheat the broiler.
Place the ciabatta on a baking sheet cut-side up. Heat it under the broiler until lightly golden brown. Combine the butter, garlic, salt and pepper in a small bowl. Slather the garlic butter over the bread and broil until bubbly and golden brown, about 2 minutes. Remove, let cool for a few minutes and cut into slices.
To serve: Bring a large pot of salted water to a boil. Cook the pasta until al dente, about 4 minutes (if using dried noodles, follow package directions). Reserve a cup of the pasta water and drain the pasta. Put about 2 cups of the sauce in a large saute pan over high heat. Add the pasta, creme fraiche, some of the pasta water and a few handfuls of the Parmigiano-Reggiano. Toss, top with the parsley and serve. Reserve remaining sauce for another use.