Preheat oven to 375F (190C). Line a 9-inch cake pan with a circle of parchment paper and brush sides and bottom with a bit of olive oil.
In a bowl, mix the sugar and zest together. Work the zest into the sugar rubbing between fingers. This releases the natural oils in the zest. Add the eggs, coconut milk, olive oil, vanilla extract and almond extract. Whisk together until smooth.
In a large bowl, whisk together the gluten-free flour, almond flour, baking powder, baking soda and salt. Add the liquids into the dry ingredients and whisk to combine. Pour into the prepared cake pan. Top the cake with the apricots while overlapping slightly.
Bake the cake until golden brown and a toothpick inserted in the center comes out clean, about an hour. Let the cake cool in the pan for 15 minutes until cool enough to handle. Invert onto a cooling rach and let cool completely before serving with chopped pistachios and dusting of powdered sugar.