Bring a large pot of generously salted water (it should taste like the sea) to a rolling boil over high heat. Add the capellini and cook until just al dente, about 2–3 minutes. Reserve 1 cup of the starchy pasta water, then drain the pasta. (The sauce will use about 1/4 cup, with extra available to adjust consistency.)

While the pasta cooks, heat olive oil and butter in a large skillet over medium heat. Add sliced garlic and red pepper flakes (if using). Sauté gently for 30–60 seconds until garlic is fragrant and just beginning to turn pale gold—do not let it brown.

Add the halved cherry tomatoes to the skillet, cut side down. Season with salt and pepper. Cook undisturbed for 2 minutes, then stir and cook for another 2–3 minutes, pressing some tomatoes gently with the back of a spoon to release their juices, until they soften and burst.

Pour the reserved pasta water, lemon zest, and lemon juice into the skillet. Stir and simmer for 1 minute, letting the liquid reduce slightly and the sauce come together.

Add the drained capellini directly into the skillet. Toss gently with tongs for about 1 minute until every strand is coated in the glossy sauce and the pasta has absorbed some flavor. Turn off the heat.

Sprinkle the torn basil and grated Parmesan over the pasta. Toss once more to combine. Divide among warm bowls or plates, garnish with extra Parmesan and basil, and serve immediately with lemon wedges.