1. Make the pasta: Stir together flour and semolina in a large bowl, and form a well in the center; pour eggs into well and stir with a fork until dough forms. Transfer dough to a work surface and knead until smooth, about 10 minutes. Cover with plastic wrap and let sit for 30 minutes.

2. Meanwhile, make the sauce: Combine tomatoes, oil, basil, garlic, and salt and pepper in a bowl; cover and let sit at room temperature for 30 minutes to meld flavors.

3. Uncover and halve dough; using a pasta roller or rolling pin, roll each piece of dough until it's 1/16" thick. Hang pasta sheets on a rack to dry slightly for 5 minutes. Slice pasta sheets crosswise into lengths of one foot and stack, one on top of another, sprinkling cornmeal in between, then roll into a cylinder; cut crosswise into ⅓"-thick ribbons. Unravel fettuccine and toss with semolina to separate; let dry for 10 minutes.

4. Bring a large pot of salted water to a boil over high heat, and add pasta; cook, stirring, until al dente, about 3 minutes. Drain pasta and add to bowl of sauce; toss to combine. Divide among serving bowls and garnish with parmesan.