Shake the can of coconut milk or stir it well (this creates a consistent thickness, since the fat often solidifies at the top of the can).
In a 3- to 4-quart saucepan or wok over medium heat, simmer 1/2 cup of the coconut milk, stirring occasionally, until reduced by about half, 3 to 5 minutes. It will get very thick and shiny and may or may not separate; either is fine.
Add the curry paste, whisk well, and cook, continuing to whisk, for 1 minute. Whisk in the broth, sugar, fish sauce, and remaining coconut milk. Bring to a simmer over medium-high heat.
Add the chicken and lime leaves, and continue to simmer, adjusting the heat as necessary. After 2 minutes, add the asparagus and oyster mushrooms and continue to simmer until everything is tender and cooked through, about 3 more minutes.
Remove the curry from the heat. Season to taste with more sugar and fish sauce, and stir in the cilantro. Transfer to a serving bowl (or serve right out of the pot). Remove the lime leaves or tell your guests to eat around them. Garnish with the red chiles and a drizzle of coconut milk.
nutrition information (per serving):
Photo: Scott Phillips