Cut kernels from 4 corn cobs; set kernels aside and reserve cobs.
Melt 3 tablespoons butter over medium heat in a large pot. Add ½ chopped onion, 3 minced cloves garlic, 2 minced chipotles, 2 teaspoons adobo and ½ teaspoon kosher salt; cook, stirring occasionally, until fragrant, about 3 minutes.
Add 1 bunch finely chopped collard greens and cook 5 minutes. Stir in 4 cups broth and reserved corn cobs; bring soup to a boil then reduce to a simmer and cook, partially covered, for 45 minutes.
Using tongs, transfer cobs to a plate; let cool.
Stir in fresh corn kernels, 1 pound chicken thighs cut into chunks, and 1 can corn and its juices; simmer until chicken is cooked through, 8–10 minutes.
Scrape back of a knife down length of cooled corn cobs to “milk” cobs; add scraped liquid and solids to soup; discard cobs.
Stir in 1½ cups half-and-half and season with salt to taste.
Serve with cilantro and lime wedges, if desired.