Trim and spiralize the zucchini (see notes below for doing this without a spiralizer). Then cut the spiralized zucchini into long noodles to be about the length of spaghetti.
Add olive oil, garlic, and the red pepper flakes to a large, deep skillet. Turn to medium heat. When the oil bubbles around the garlic, add the zucchini noodles.
Toss the noodles with pasta tongs and cook until al dente — they should be wilted but still have a crunch; 5 to 7 minutes. Do not let the noodles cook any longer, or else they will become mushy. As they cook, keep tossing so that all the zucchini noodles have a chance to hit the bottom of the skillet.
Stir in the tomatoes, basil, and parmesan cheese, and then cook for one minute. Use pasta tongs to transfer the noodles, tomatoes, and basil to a serving dish. Leave the liquid in the skillet.
Bring the liquid left in the skillet to a simmer.
Combine cornstarch and cold water in a small bowl, then whisk into the simmering liquid. Cook while whisking until the liquid thickens to a sauce; about 1 minute. Taste the sauce and season with salt.
Pour the sauce over the zucchini, tomatoes, and basil. Finish with more parmesan cheese on top and serve immediately.
