Spiralize the zucchini and lay the noodles on paper towels; blot off surface moisture — less moisture in the pan means no watery zoodles. Pat the chicken pieces dry, then season with 1/2 teaspoon salt and 1/4 teaspoon pepper.

Heat 3 tablespoons butter in a large skillet over medium-high heat until foaming. Add the chicken in a single layer and sear undisturbed for 3 minutes, then flip and cook 3–4 more minutes, until golden and an instant-read thermometer reads 165°F. Transfer to a plate.

Reduce the heat to medium. Add the remaining 3 tablespoons butter, the garlic, and the red pepper flakes (if using). Cook, stirring constantly, for 1 minute — the garlic should smell fragrant and turn pale gold, not brown. Stir in the lemon zest and juice, scraping up the browned bits.

Add the zucchini noodles and toss in the garlic butter for 2 minutes, just until they soften slightly but still have bite. Do not walk away; the don't-overcook rule is the whole recipe here.

Return the chicken (and any juices) to the skillet. Sprinkle over the Parmesan and toss 1–2 minutes, until everything is glossy and the cheese melts into the sauce. Season with the remaining salt and pepper.

Stir in the cherry tomatoes and basil, if using, and warm through 1 minute. Serve right from the skillet with extra Parmesan and lemon wedges.