Place the olive oil, sunflower oil, cognac, orange juice, and granulated sugar in a large bowl. Mix thoroughly with a hand whisk.
Place the flour, baking powder, baking soda, and orange zest in another large bowl. Mix thoroughly.
Gradually add the wet ingredients to the bowl with the dry ingredients. Carefully mix by hand until it turns into a nice cookie dough. DO NOT over-mix, or else the oils will start to seep out of the dough.
Shape the cookie dough into 30 g/1 oz round balls and then flatten them a little to give them the traditional melomakarona cookie appearance. Transfer to a rimmed baking sheet lined with parchment paper.
With a fork, pierce small holes on the surface of each cookie. This will help the cookies bake faster and soak up the syrup easier.
Bake for 20-25 minutes, until golden and crunchy.
When ready, remove from the oven and immediately dip the hot Melomakarona cookies in the syrup for 10 seconds. Transfer to a platter with a slotted spoon and sprinkle with ground walnuts.
Serve as they are or coat with chocolate ganache.