Creamy coconut milk and a touch of sugar help to round out this fragrant and rich sauce, heady with the scent of lime and lemongrass.
Pour aromatics and pan drippings through a fine wire-mesh strainer into a medium bowl, pressing on solids. Discard solids. Skim off and discard fat from drippings (there should be about 1 cup drippings remaining; top up with chicken stock, if needed).
Transfer drippings to a blender; add coconut milk, butter, lemongrass, and brown sugar. Process until smooth, about 30 seconds. Set aside 2 tablespoons coconut milk mixture. Pour remaining coconut milk mixture into a small saucepan. Stir together cornstarch and reserved 2 tablespoons coconut mixture. Bring coconut milk mixture in saucepan to a simmer over medium; stir in cornstarch mixture. Simmer, stirring often, until slightly thickened, about 2 minutes. Serve with Dry-Brined Spatchcocked Turkey.