Arrange the squash in a single layer in the shallow water; season with salt. Cover, bring to a boil over high, and cook for 5 minutes. Scatter the broccoli on top of the squash, season with salt, then pile the kale on top of the broccoli and season with salt. If the water has evaporated, add another ¼ inch of water. Cover and cook until the squash is tender and the broccoli is bright green and crisp-tender, 2 to 4 minutes. Turn off the heat but keep the skillet covered while you peel the eggs.
