Place ground coffee in a clean glass container. Pour hot water over coffee; let stand 10 minutes. Stir in the cold water. Cover and refrigerate for 12-24 hours. (The longer the coffee sits, the stronger the flavor.)
Meanwhile, for coconut simple syrup, in a small saucepan, bring water, sugar and coconut to a boil. Reduce heat; simmer 10 minutes. Strain and discard coconut. Cool completely.
Strain coffee through a fine-mesh sieve; discard grounds. Strain coffee again through a coffee filter; discard grounds. Store coffee in the refrigerator for up to 2 weeks. For each serving, fill a large glass with ice. Add 1 cup cold-brewed coffee and 4 tablespoons coconut syrup; stir. Top with 2 tablespoons coconut milk.