- 2 tablespoons olive oil
- 1 medium onion, coarsely chopped
- 1/4 cup finely chopped fresh cilantro stems
- 2 garlic cloves, coarsely chopped
- 1 (2 1/4-pound) piece calabaza squash or 1 (2 1/2-pound) whole kabocha squash, peeled, seeded, and cut into 1/2-inch pieces (6 cups)
- 4 cups water
- 1 1/4 cups well-stirred canned unsweetened coconut milk (12 ounces)
- 3 ears of corn (fresh or thawed frozen), kernels cut off and reserved for relish (below) and cobs halved crosswise
- 2 teaspoons salt
- 1/4 teaspoon cayenne
- 4 1/2 teaspoons fresh lime juice
- 1/4 teaspoon salt
- Pinch of sugar
- 2 tablespoons olive oil
- 2 cups corn kernels (see above)
- 2 tablespoons coarsely chopped fresh cilantro
- 1 tablespoon finely chopped shallot
- Heat oil in a 4- to 5-quart heavy pot over moderately high heat until hot but not smoking, then sauté onion, stirring occasionally, until beginning to soften and edges are browned, about 4 minutes. Add cilantro stems and garlic and cook, stirring occasionally, 3 minutes. Add squash pieces and cook, stirring frequently, 3 minutes. Stir in water, coconut milk, corn cobs, salt, and cayenne and simmer, uncovered, stirring occasionally, until squash is very tender, about 15 minutes.
- Whisk together lime juice, salt, and sugar in a bowl, then add oil and whisk until combined.
- Cook corn kernels in a saucepan of boiling salted water until just tender, 2 to 3 minutes. Drain in a sieve, then rinse under cold water to stop cooking. Drain well, then transfer to dressing along with cilantro and shallot and toss well to coat.
- Discard corn cobs, then purée soup in batches in a blender (use caution when blending hot liquids) until smooth, transferring to a 2-quart measure.
- Divide soup among bowls and gently stir 1/4 cup corn relish into each.