Whisk turmeric, cardamom, black pepper, ginger, cloves, and allspice together in a small bowl.
Heat milk in a small saucepan over medium heat until heated through, 3 to 4 minutes; stir honey and vanilla extract into milk until completely dissolved. Whisk 1 teaspoon turmeric mixture into milk mixture; reduce heat to medium-low and cook until flavors blend, 2 to 3 minutes. Pour mixture through a strainer.
