Prepare the Mixing Bowl: In the bowl of a stand mixer, combine the eggs and salt.
Whisk Eggs: Using a whisk attachment, beat the eggs and salt on medium speed for 1-2 minutes until well mixed and slightly frothy.
Add Flours: Remove the whisk attachment. Add both the all-purpose flour and semolina flour to the egg mixture.
Initial Mixing: Attach the dough hook to your stand mixer. Mix on low speed (Speed 2) for 1 minute until the flours are mostly incorporated and the mixture looks shaggy and crumbly.
Knead the Dough: Continue mixing with the dough hook on medium-low speed (Speed 3) for 5-7 minutes. The dough will look crumbly initially but should gradually come together into a shaggy ball. It should feel firm but slightly pliable. If the dough is too dry and not coming together, add water 1 teaspoon at a time until it just forms a cohesive, firm dough. Avoid adding too much water, as this can make the pasta sticky.
Rest the Dough: Transfer the dough from the mixer bowl. Gently press it together to form a rough ball. Wrap the dough tightly in plastic wrap to prevent it from drying out. Let it rest at room temperature for at least 30 minutes, or up to 1 hour. This resting period allows the gluten to relax, making the dough easier to extrude.
Set up Extruder: While the dough rests, prepare your KitchenAid stand mixer with the extruded pasta attachment, selecting your desired pasta die (e.g., spaghetti, rigatoni, macaroni).
Extrude Pasta: Once rested, unwrap the dough. Cut the dough into smaller pieces (about golf ball size) that will fit easily into the hopper of your extruder. Turn the mixer to medium speed (Speed 4-6, depending on your machine and desired extrusion speed) and feed the dough pieces into the attachment. As the pasta extrudes, gently guide it and cut it to your desired length using a knife or the built-in cutter, if available.
Dry Pasta (Optional): As you extrude, lay the fresh pasta on a lightly floured baking sheet, a pasta drying rack, or hang it to dry slightly. This prevents sticking. For best results, allow the pasta to dry for 15-30 minutes before cooking.
Cook Pasta: Bring a large pot of heavily salted water to a rolling boil. Add the fresh pasta and cook for 2-4 minutes, or until al dente. Fresh pasta cooks much faster than dried pasta, so taste frequently.
Serve: Drain the pasta and toss immediately with your favorite sauce.