This dessert invites you to uncover its secrets layer by layer. Passion fruits might be unfamiliar, but they're easy to use. We scoop out the pulp and edible seeds and spoon them over each parfait.
Make panna cotta: Bring 1 cup coconut milk and the cream to a simmer in a medium saucepan over medium-low heat. Remove from heat, and add ginger. Cover, and let steep 30 minutes. Pour mixture through a fine sieve into a clean medium saucepan; discard ginger.
Sprinkle 1 teaspoon gelatin over 1 1/2 tablespoons cold water in a small bowl, and let stand 2 minutes to soften. Whisk gelatin mixture and 1/4 cup sugar into coconut-milk mixture. Cook over medium heat, stirring, until sugar and gelatin have dissolved. Pour 1/2 cup panna cotta into each of six glasses. Refrigerate until firm, about 2 1/2 hours.
Make gelee: Sprinkle remaining 3/4 teaspoon gelatin over passion-fruit juice in a small saucepan; let stand 2 minutes to soften. Whisk in 1 teaspoon sugar. Cook over medium-low heat, stirring, until gelatin and sugar have dissolved. Pour through a fine sieve into a glass measuring cup; let cool, about 10 minutes. Pour 3 tablespoons gelee into each glass. Refrigerate until firm, about 1 1/2 hours.
Meanwhile, make tapioca: Tie cardamom, peppercorns, and bay leaf in a square of cheesecloth to make a bouquet garni. Bring whole milk and remaining cup coconut milk to a simmer in a medium saucepan over medium-low heat. Add bouquet garni, remaining 1/2 cup sugar, and the tapioca; bring to a simmer over medium heat, stirring. Continue to cook, stirring often, until tapioca pearls are tender, 35 to 40 minutes (consistency will be loose). Discard bouquet garni. Cover tapioca; let cool to room temperature, or refrigerate until ready to serve.
Just before serving, if you prefer a thinner tapioca, stir in up to 1/2 cup milk. Divide tapioca among glasses over gelee. Halve passion fruits, and spoon pulp and seeds over each parfait.
Unless they're wrinkled, passion fruits aren't ripe. If their skin is smooth, let them sit at room temperature for a few days.