Add 00' flour, whole eggs, egg yolks, and fine sea salt to a mixing bowl. Using clean hands, mix the ingredients together just until a shaggy dough forms.
Pour the shaggy dough onto a clean work surface and gently knead/pat the excess flour together to form one solid dough.
Shape the pasta dough into a square. Wrap the dough in plastic wrap and allow to rest until you touch the dough and it has slightly softened, about 30 - 35 minutes.
Cut the dough into 3 equally sized pieces. Use your hands or a rolling pin to slightly flatten the pasta dough so it can fit into the widest setting of the pasta machine. Dust each side of the pasta with semolina to ensure it doesn’t stick.
Pass the pasta dough through the widest setting on the pasta machine. Fold each side of the pasta to the middle, then pass the pasta dough through the widest setting again.
Reduce the pasta machine width setting by one, then continue to pass the pasta through the machine. Continue flattening the pasta, reducing the setting by one, until it reaches a medium setting, about 1 mm thick (for me setting 7). You can add additional semolina flour throughout this process if the dough starts to get sticky.
Use the pasta machine attachment to cut the pasta into thin, tagliatelle shapes (about 7 mm wide).
Dust the pasta with semolina flour to prevent sticking then shape the pasta into a nest before placing it on a sheet tray filled with semolina flour.
Boil a pot of water and generously season with coarse sea salt. Cook pasta for 30 seconds - 2 minutes, until slightly softened. Finish cooking with sauce of choice.