Preheat the oven to 350F.
Grease a 9x9 pan with butter.
Melt the butter, and set aside to cool.
Beat together the eggs, sugar, milk, cream, baking powder, and vanilla extract in a large bowl.
Add the butter in and mix thoroughly to avoid cooking the eggs.
Whisk in the cornstarch and coconut slowly.
Pour the batter into the pan and bake for 30 minutes.
Combing the sugar and lemon juice with 1/2 cup of water in a small pot over medium heat.
Stir the mixture until the sugar is completely dissolved and bring to a simmer.
Add in the rose water and let the syrup simmer for a few minutes.
Rosewater is a very floral and distinctive ingredient. I enjoy it very much and reduced the original amount by half. Be cautious when using this ingredient and listen to your senses to use the right about for you.