Place an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Spray a heavy baking sheet with vegetable oil cooking spray.
Arrange the prosciutto in a single layer on the prepared baking sheet. Bake for about 10 minutes until crispy. Drain on paper towels. When cool enough to handle, crumble the prosciutto into 1/2-inch pieces.
Cut the pasta dough in quarters and press flat. Run each piece of pasta dough several times through a pasta-rolling machine, adjusting the setting each time until the pasta is about 1/16-inch thick. Add the fettuccine attachment and run the pasta sheets through. Dust the fettuccine lightly with flour to avoid sticking.
Bring a large pot of salted water to a boil over high heat. Add the olive oil and pasta. Cook until tender but still firm to the bite, stirring occasionally, 4 to 5 minutes. Place the pasta in a large serving bowl.
For the sauce: In a medium saucepan, combine the figs, broth, orange juice, thyme, salt and pepper. Bring to a boil over medium heat. Reduce the heat and simmer for 5 minutes. Remove the pan from the heat. Stir in the goat cheese, mascarpone cheese and lemon zest until the sauce is creamy.
Pour the sauce over the cooked pasta and toss until all the ingredients are coated. Top with the crumbled prosciutto and serve.
Place the cake flour, all-purpose flour, egg yolks and salt in a food processor. Pulse to combine. With the machine running, gradually add the oil then 1/3 to 1/2 cup water until the mixture forms a dough (the dough should stick together if pinched between your fingers). If necessary, add additional water, 1 teaspoon at a time if the dough is too dry.
Place the dough on a lightly floured surface. Gather the dough into a ball and knead until the dough is smooth, 5 to 8 minutes. Cover with plastic wrap and refrigerate for 30 minutes.
Cut the dough into quarters and press flat. Run each piece of pasta dough several times through a pasta-rolling machine, adjusting the setting each time, until the pasta is about 1/8 to 1/16-inch thick. Cut the pasta into the desired shape and use as needed.
Recipe can also be made with 1 pound dried fettuccine pasta. Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes. The pasta dough can be rolled out by hand. Cut the chilled dough into quarters and using a rolling pin, roll out the dough until 1/8- to 1/16-inch thick.