Pulse the flour, semolina and salt in a food processor. Add the eggs, olive oil and herbs and pulse until the dough forms. Shape the dough into a round disk and cover with plastic wrap. Allow the dough to rest at room temperature for 30 minutes or refrigerate overnight. (If the dough is refrigerated, let it sit at room temperature for 20 minutes before rolling out the pasta.)
Divide the pasta dough into 4 pieces keeping them covered. Working with one piece of dough at a time, flatten slightly and feed through the smooth rollers of a pasta machine starting at the widest setting. Fold the pasta sheet in half each time it is fed through at a narrower setting until the pasta sheet is very thin but does not tear. (You can also roll out the pasta by hand with a rolling pin on a well-floured work surface.) Place the pasta sheets on a floured work surface to dry for 10 minutes.
Cut the pasta sheets into 12-inch lengths. Sprinkle with flour and roll them up loosely. Using a knife, trim the rough edges and cut into 1-inch wide strips. Unroll and place the strips on a baking sheet lined with waxed paper. Repeat with the remaining dough.
Bring a large saucepan of salted water to a boil. Cook the pasta for 2-3 minutes until al dente.
Heat the olive oil in a large skillet over medium high heat, cook the garlic until fragrant, about 30 seconds. Toss the pasta into the oil before transferring to a large bowl and stirring in the tomatoes, zucchini, mozzarella, chives, salt and pepper.