Prepare a grill for medium-high heat. Combine tomatillos and chiles on a rimmed baking sheet. Drizzle with a bit of oil, season with salt, and toss to coat. Grill, turning occasionally, until lightly browned all over, 8–10 minutes for tomatillos and about 4 minutes for chiles. Return to baking sheet; let cool.
Purée tomatillos and 2 chile halves in a blender until smooth. Add lime juice; taste and season with salt. Set remaining chiles aside for serving.
Do Ahead: Aguachile can be made 2 days ahead. Cover and chill. Bring to room temperature and stir in a splash of water to loosen before using.
Arrange mangoes, onion, tomatoes, and hearts of palm on a platter. Drizzle aguachile over and top with cilantro and reserved chiles.
