Let me eat cake

As a result of an unaccustomed amount of time on my hands, and as a panacea for the many pitfalls that overcome those who take on building projects in Bodrum in winter; we are eating a lot of cake.  A homemade creation in the cake tin is one of those little luxuries I promised myself when I stopped working.  Unfortunately, it doesn't stay in the tin very long.  I've just shipped all my clothes from England to Turkey and I want to be able get into them in the summer, so I've been reviewing my cake recipes and seeing if I can knock off a few hundred calories without spoiling the taste.  I'm experimenting by using pekmez, instead of oil and sugar. For those who don't live in the Near East, pekmez is grape syrup produced by boiling grape juice, or occasionally mulberry juice, until it thickens. It is known as petimezi in Greece and mosto d'uva in Italy. It is a good source of iron and calcium so I'm sure it must be better for us than white sugar.  If you can't find it, I think maple syrup would work just as well.  There is still a little oil and sugar in this recipe but much less than the original.

Heat oven to 170 °C.
Beat together 4 eggs, 1 cup pekmez, ¼ cup oil, ½ cup sugar,1 tsp cinnamon, 1tsp vanilla sugar.
When well mixed, (I use an electric mixer for about 5 minutes) add 1 cup sultanas, 1½cups flour, 1/2 cup oat bran,  2 tsp baking powder and 2 cups  grated carrot and stir well.
Pour into a greased 8 inch, loose bottom, cake tin and bake on a low shelf for 1 hour.  I cover mine with a silicon baking sheet for the first 30 minutes to stop the top cooking too fast.  The cake is done when the top of the cake bounces back when touched. It may take between 50 minutes and 90 minutes, depending on your oven.  I think it tastes better than the sugar and oil-heavy version.  We haven't the will-power to find how long it keeps in the tin.