Cook the spaghetti according to the package directions; drain, reserving 1 cup cooking water.
Melt the butter in a large skillet over medium-high heat. Add the zucchini noodles, lemon zest, red pepper flakes and 1 teaspoon salt. Cook, tossing gently with tongs, until crisp-tender, about 2 minutes. Add the pasta and reserved cooking water and toss to combine. Stir in the lemon juice and Parmesan. Season with salt.
Transfer the spaghetti to a serving bowl. Top with more Parmesan and red pepper flakes and serve with lemon wedges.
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