1 cup all-purpose flour, plus more for dustingPasta and Assembly2 large red sweet peppers or 1 large red bell pepper, halved lengthwise, seededKosher salt, freshly ground pepperPurple or green basil leaves or parsley leaves with tender stems, torn Combine 1 cup plus 2 Tbsp. semolina flour and 1 cup all-purpose flour in a large bowl. Purée eggs, basil, and 1 tsp. salt in a blender on medium-high speed, scraping down sides as necessary, until mixture is smooth, about 30 seconds.
Cut dough into 6 equal pieces. Working with one piece at a time, lightly dust both sides with all-purpose flour and roll into a thin 5½x20" rectangle . Dust both sides of dough with semolina flour and loosely roll into a cylinder. Using a sharp knife, trim edges and discard. Cut dough into 1½"-wide slices. Unfurl noodles, dust with semolina flour, and gently toss to separate. Place on a rimmed baking sheet and cover with a clean kitchen towel.Preheat oven to 425°.
Combine cherry tomatoes, 2 Tbsp. oil, and remaining garlic clove in a small bowl. Season with salt and pepper and let sit at room temperature 30 minutes. Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente, about 4 minutes. Drain, reserving 1 cup pasta cooking liquid.
Toss pasta with tomato and pepper mixture, adding ⅓ cup pasta cooking liquid and remaining 2 Tbsp. oil to keep pasta from sticking; add more pasta cooking liquid if necessary. Divide pasta among plates, then top with cherry tomato mixture and any accumulated juices, basil, and Parmesan.