Combine the rice, water, and 1 1/2 cups of dairy-free milk in a small saucepan. Cover and bring to a boil. Once boiling, lower the heat to low. Simmer for approx. 10 minutes, until the rice is al dente.
Add the cocoa, cinnamon, salt, and chocolate. Stir until chocolate is melted and fully combined. Stir together the honey, vanilla, and remaining 1/2 cup of dairy-free milk. Add to the rice mixture. Stir constantly for about 5 minutes. Pudding will begin to thicken. Add more milk if it seems too thick.
Remove saucepan from the heat and allow to cool. Cover and chill for at least an hour before serving.