Refrigerate 1 can coconut milk overnight.
Place the chocolate chips in a medium bowl. In a small saucepan, heat 1 cup room-temperature coconut milk over medium until warm, about 3 minutes. Add the cornstarch and salt; whisk until dissolved. Cook, stirring constantly, until mixture thickens, about 2 minutes. Stir in 1/2 cup beet juice; whisk 1 minute more. Strain into the chocolate chips; let stand 1 minute, then whisk until the chocolate is smooth.
Divide the chocolate among six 6-oz. ramekins. Chill until cold, at least 1 hour, or cover and chill up to 4 days.
Scoop the thick cream from the top of the refrigerated coconut milk into a medium bowl. Add the remaining 1 tsp. beet juice and the confectioners' sugar and vanilla. Using an electric mixer, beat on high until peaks form, 3 to 5 minutes. Spoon a dollop of whipped coconut cream on top of each pudding.