Preheat oven to 180°C.
For the peach compote
Place sugar, water, lemon juice in a saucepan and bring to a boil, stirring occasionally until the sugar dissolves. Add the peaches, reduce heat and cook for 5 minutes until soft. Remove the compote from the heat and let it cool completely.
Take a little less than half of the peach slices, cut into small cubes and set aside.
For the crust
Place the ground biscuits, sugar, melted butter and almond extract in a bowl and mix them well. Spread the mixture in a spring-form pan (9” diameter) and refrigerate.
For the cake
In the bowl of an electric mixer, add the cream cheese, feta cheese and sugar and mix for 1-2 minutes, until they blend evenly together.
Add the eggs one by one, the lemon juice, vanilla extract, flour, salt and finally the cubed peaches. Beat well to blend all ingredients. Pour the filling into the biscuit base and bake in preheated oven for 1 hour.
Remove from oven and let cool completely.
Place the cheesecake on a platter, and top with the peach compote.