Bring aquafaba to a boil in a small saucepan over medium heat. Lower heat to medium-low and simmer until reduced to 1/2 cup.
Pour aquafaba into bowl of a stand mixer or a medium bowl, then whisk in granulated sugar. Chill until completely cool, at least 2 hours.
Preheat oven to 225°. Line a baking sheet with parchment paper. Add cream of tartar to cooled aquafaba and, using the whisk attachment of a stand or hand mixer, whip on high until stiff peaks form, about 8 minutes. Reduce speed to low and gradually beat in powdered sugar and salt. Return to high speed and whip until stiff, glossy peaks form, about 2 minutes more. Beat in vanilla, whip 1 minute more.
Using a rubber spatula, spread scoops of meringue into 5 to 6 disks (each about 4 in. wide and 3/4 in. thick) on parchment paper. Using back of a spoon, make a slight depression in middle of each. Bake until crisp on outside, 2 1/2 to 3 hours, depending on whether you like them slightly chewy in the center or crisp throughout.
Meanwhile, make pomegranate coconut cream: Pour pomegranate juice into a microwave-safe container and microwave 5 minutes. Let cool.
Spoon off creamy layer at top of coconut-milk can into a chilled mixing bowl. Beat cream with a mixer on high speed for 30 seconds, then reduce speed to low and gradually beat in sugar and vanilla until incorporated. Stir in reduced pomegranate juice and cool until ready to use.
To assemble, place each meringue on a dessert plate. Spoon on about 2 to 3 tbsp. pomegranate-coconut cream onto each, then sprinkle with pomegranate seeds and chocolate shavings.
Note: Nutritional analysis is per pavlova.