In a dry saucepan, heat ¾ cup sugar over medium heat, stirring gently until it melts and becomes a deep amber color, about 8–10 minutes. Once golden brown, pour into a 9-inch cake pan, tilting to coat the bottom evenly. Set aside to cool and harden.

In a large mixing bowl, whisk together 10 egg yolks, 1 can sweetened condensed milk, 1 can evaporated milk, and 1 tsp vanilla extract until smooth. Strain through a fine sieve and pour over the cooled caramel.

In a separate bowl, combine 1 cup cake flour, 1½ tsp baking powder, and ¼ tsp salt. Whisk until evenly blended.

In another mixing bowl, whisk together 5 egg yolks, ¾ cup sugar, ¼ cup oil, ⅓ cup ube halaya, ½ tsp ube extract, and ⅓ cup water until smooth. Gradually add dry mixture; stir gently until fully incorporated.

In a clean bowl, beat 5 egg whites with ¼ tsp cream of tartar until soft peaks form, then gradually add ¾ cup sugar until whites are stiff and glossy, about 3–5 minutes.

Gently fold the whipped egg whites into the prepared ube batter in thirds, using a light hand until just combined.

Pour ube chiffon batter slowly over flan mixture in the cake pan. Place in a larger roasting pan, add hot water until it reaches about 1 inch deep. Bake at 350°F (175°C) for 1 hour.

Once baked, let cool in the pan for 10 minutes. Invert onto a serving plate. Refrigerate for at least 4 hours, preferably overnight.