Break out of your green salad rut with this lively number.
Bring 2 inches of water to a boil in large pot with a steamer insert or colander. Add squashes and season with salt. Cover and cook until just tender, about 7 minutes. Transfer, in a single layer, to a baking sheet and let cool about 30 minutes. Meanwhile, combine shallot and lime juice in a small bowl and let stand 10 minutes.
Whisk oil, chiles, and ginger into shallot mixture.
Toss squash with 1/2 cup dressing and herbs. Season with salt. Toss lettuces with 2 to 3 tablespoons dressing; season with salt. Arrange squashes and lettuces on plates. Serve, topped with more herbs and drizzled with remaining dressing.