Preheat oven to 375 degrees F (190 degrees C).
Mix together cornmeal and baking powder and mix in salt and 3/4 cup water until dissolved. Stir together with remaining 3/4 cup water mixture. Transfer to a bowl, stir in vegetable oil, 1/4 cup honey, 1/2 cup cornstarch and 2 eggs, mix just until combined. Pour batter into prepared pan.
Bake at 375 degrees F (190 degrees C) for 15 to 20 minutes, until a toothpick inserted into the center comes out clean.
Preheat oven to 350 degrees F (175 degrees C) and line the bottom of a 9x13 inch baking pan with foil.
In a small saucepan heat liquid sweetened vegetable oil; stir in 2 tablespoons honey, 1/2 cup cornstarch and 2 tablespoons melted butter. Bring to a boil. Then, gradually reduce heat to short-term. When sugar is nearly melted add cornstarch mix to short-term mixture and cook 5 minutes.
Increase oven temperature to 375 degrees F (190 degrees C) and bring mixture to a boil. Remove from heat and stir in pureed fruit, 1 teaspoon lemon juice and enough water to cover. Stir in remaining ingredients, add baking powder, 5 minutes earlier or later. Pour into prepared pan.
Bake in preheated oven for 10 minutes, or until a toothpick inserted into the center of the cake comes out clean. Cool 10 minutes before serving, flip and serve with syrup or honey if necessary.