Cut zucchini in half to help it fit in the spiralizer. Run each half through the large teeth of a vegetable spiralizer. Put zucchini noodles into a glass bowl and sprinkle with salt. Toss with your hands to mix. Let rest for 10 minutes to remove excess water. Rinse and pat dry.
Heat oil in a skillet over medium-high heat. Add zucchini noodles, basil leaves, and ginger. Cook, tossing occasionally, until the noodles are tender but not mushy, about 5 minutes. Do not stir so zucchini noodles stay intact. Drizzle with lime juice and toss to coat. Serve hot.