Combine flour, salt and semolina in a bowl. Combine eggs, yolks and oil in a separate bowl. Gradually add egg mixture to flour mixture, mixing slowly with a fork until mixture comes together. Using your hands, rub mixture until combined and crumbly then knead into a firm dough. Wrap tightly in plastic wrap and refrigerate overnight.
The next day, bring the dough to room temperature. Divide dough into four pieces. Working with one piece at a time, flatten then roll through a pasta machine, starting at the widest setting and dusting with extra flour and semolina as needed. Fold in half and repeat until pasta is smooth and silky, then continue rolling and folding, reducing the settings notch by notch until dough is 2mm thick. Cut dough into manageable sheets and layer on a tray between sheets of baking paper dusted with semolina. Refrigerate for 30 minutes.
Cut dough into 4.5cm squares. Take a square and pinch two of the opposite corners together to make a triangle. Take the remaining two sides and pinch together in the opposite direction to make the sopressini shape. Place on a tray and toss with some of the extra semolina.
Cook sopressini in a large saucepan of boiling, salted water until it floats to the top and is al dente (2-3 minutes). Drain and return to pan. Add pesto alla Trapanese and toss gently to combine. Sprinkle with parmesan to serve.