Combine coconut milk, coconut cream, evaporated milk, cinnamon, nutmeg, and ginger in a large saucepan.
Mix milk and cornstarch together in a bowl until dissolved; stir into coconut milk mixture. Add sugar, vanilla extract, orange blossom water, salt, and lime zest to coconut milk mixture; cook, stirring constantly, over medium heat until simmering and mixture begins to thicken, about 5 minutes. Lower heat to medium-low and cook until thickened, about 15 minutes.
Remove saucepan from heat, pour mixture into a deep 9-inch cake pan, and cool to room temperature, about 30 minutes. Cover pan with plastic wrap and refrigerate until tembleque is chilled, at least 4 hours to overnight.
Remove tembleque from refrigerator and allow to sit at room temperature, about 10 minutes. Dip bottom of pan in a bowl of warm water for 1 minute. Carefully separate tembleque from pan by running a thin knife around the edges. Place a serving dish on top of pan and invert tembleque onto dish; garnish with cinnamon.