Whisk the agave nectar, cornstarch and salt in a heavy-bottomed pot. Whisk in the evaporated milk and egg whites until well combined. Cook over medium-low heat, whisking constantly, until the mixture bubbles and thickens, about 10 minutes. Remove from the heat; stir in 1 tablespoon vanilla.
Transfer 1 cup of the mixture to a medium bowl. Add the white chocolate chips and the remaining 1 teaspoon vanilla and stir until the chips melt. Add the cocoa powder and semisweet chocolate chips to the remaining pudding and stir until the chips melt.
Divide the chocolate pudding among dishes and top with the vanilla pudding. Cover with plastic wrap and refrigerate until set, at least 2 hours. Chop some chocolate chips to sprinkle on top.