Spiralize the zucchini (see blog post above for tips). Set aside.
In a small bowl or large liquid measuring cup, whisk together the lemon juice and cornstarch. Set near your stove.
In a large skillet, melt the butter over medium heat. Add the shallots and saute until soft, about 3 minutes.
Add the garlic and cook just until very fragrant, about 30 seconds.
Add the cherry tomatoes and stir to coat. Let cook 2 minutes, just until the tomatoes begin to soften.
Add the lemon juice mixture and red pepper flakes. Let simmer 1 minute.
Add the zucchini noodles. Toss them with the mixture, using a pair of tongs to coat them as evenly as possible with the sauce and to break apart the noodles. At first the mixture will seem dry.
Add the Parmesan cheese. Keep tossing and cooking. As the zucchini cooks and gives up its liquid, it will form a sauce that coats the pasta. Continue to cook and toss, until the zucchini noodles are al dente, about 4 minutes.
Add a good pinch of salt and several grinds of pepper, then toss in the basil. Taste and adjust seasoning as desired. Serve right away, topped with extra Parmesan cheese.
TO MAKE AHEAD: Spiralize the zucchini noodles up to 2 days in advance, and store them in an airtight storage container in the refrigerator.
TO STORE: Refrigerate leftovers in an airtight storage container for up to 3 days.
TO REHEAT: Gently reheat leftovers in a large skillet on the stovetop over medium-low heat or in the microwave.