• Lightly-grease 4 large llaneras with melted butter or cooking spray.

For the Ube Halaya

• In a wide, heavy-bottomed pan over medium heat, combine grated ube, coconut milk, condensed milk, evaporated milk, condensed milk, butter, and sugar.
  
  
• Bring to a boil, stirring occasionally until sugar is dissolved, butter is melted, and ube is dispersed.
• Add ube extract, if using, and stir until mixture is evenly colored.
• Lower heat and continue to cook, stirring regularly, for about 30 to 40 minutes or until a soft, sticky dough forms.
• Add cheese and stir until melted.
• Continue to cook for another 10 to 15 minutes or until mixture is thick enough to cling to the back of the spoon and pulls slightly from the side of the pan.
• Remove from heat and divide equally into the four prepared llaneras. Use an offset spatula to press and flatten the ube evenly.
  
  

For the Leche Flan

• In a large bowl, combine egg yolks, evaporated milk, and condensed. Stir in a circular motion until well-blended.
  
  
• Using a fine-mesh sieve or cheesecloth, strain mixture.
• Using a ladle, evenly pour the flan mixture over the ube halaya base in the laneras up to ¾ full.
• Cover the llaneras tightly with aluminum foil and steam for 30 to 40 minutes or until the custard is set and a toothpick inserted in the center comes out clean.
• Remove from heat and allow to cool before adding merinque layer.

For the Meringue Layer

• In a bowl of a stand mixer, beat the egg whites until frothy.
  
  
• Add the cream of tartar and continue to beat until soft peaks form.
• Gradually add the sugar and keep beating until the mixture form firm peaks.
• Gently spread over the leche flan until each lanera has a heaping mound of meringue on top.
• Use an offset spatula to smoothen the meringue. Run the tines of a fork lightly on the meringue to make decorative lines.
• Bake in a 350 F oven for about 15 to 20 minutes or until meringue is golden brown. Keep from opening and closing the oven door to prevent the meringue from deflating.
• Remove the cake from heat and chill for 8 hours to overnight before serving.