With a hand-mixer mix the eggs with the sugar. Add also the vanilla sugar. Mix until it gets foamy.
Add the cream cheese, the heavy cream and the lemon/lime zest if you have decided to add some. ( I know many dessert lovers who do not like lemon zest that is why it should be up to you if you wish to add some.)
Pour the cheese layer mixture in the springform and spread evenly.
If you are not sure about the springform you have if it is really leaking free you can use a sheet of aluminum foil and wrap the springform to avoid water going through.Use a large roasting pan to fill up with hot water and put the springform in it. Bake in a preheated oven for 1h and 15 min. After 45 min. Baking time cover the cheesecake with a baking sheet so it does not get burned or the edge of the cheese layer gets too dry.
After turning off the heat open the oven, if possible just 5-6 cm., and let the cheesecake completely cool down in the oven. Otherwise, it might break in the middle due to sudden change of the temperature.
After cooling down put the cheese cake in the fridge for at least 5 hours. You can wrap the form in clear wrap in order to protect the cake of catching some other aroma out of your fridge.
Wash and dry the strawberries and cut them in slices. Top up the cheesecake with strawberries.