Roast corn on rack of gas burner over high heat, turning occasionally with tongs, until kernels are charred in spots, 4 to 5 minutes. (Alternatively, heat a dry well-seasoned cast-iron skillet and roast corn over moderately high heat, turning occasionally, about 10 minutes.)
Transfer corn to a cutting board and, when cool enough to handle, cut kernels from cob with a sharp knife, then cut cob into thirds.
Bring kernels, cob pieces, 4 cups water, garlic, salt, and 1/2 cup onion to a boil in a 3-quart saucepan and boil until liquid is reduced to about 3 cups, about 20 minutes.
Remove from heat and cool, uncovered. Discard cob pieces.
Purée corn mixture along with chile and remaining 3/4 cup onion in a blender, then pour through a fine-mesh sieve into a bowl, pressing hard on and then discarding solids. Return broth to cleaned blender.
Quarter, pit, and peel 1 avocado, then add to blender with 2 tablespoons lime juice and purée until smooth.
Transfer soup to a bowl and cover surface with plastic wrap. Cover bowl with plastic wrap and chill soup at least 1 hour.
Purée cilantro, oil, and salt in cleaned blender, scraping down sides of blender several times.
Pour oil into cleaned fine-mesh sieve set over a bowl and let drain 15 minutes (do not press on solids). Discard solids.
Halve and pit remaining avocado and scoop small balls from flesh with melon-ball cutter, then toss gently with remaining tablespoon lime juice in a bowl.
Whisk together crema and remaining 2 tablespoons water in a small bowl until smooth.
Season soup with salt and ladle into 6 shallow soup bowls. Divide avocado balls among bowls, then drizzle with crema and cilantro oil.
•Soup can be chilled up to 1 day.•Cilantro oil can be made 3 hours ahead and chilled, covered.
