In a large bowl, mix the flour, baking powder, and baking soda, ground cloves, and cinnamon together.
In a separate bowl, combine the extra virgin olive oil, orange juice, brandy, zest of orange, lemon juice, and sugar. Mix well.
Slowly, add the dry flour mixture to the wet olive oil mixture. Using your hands, slowly knead the dough until all the flour has been added. Do not overwork the dough, but make sure the final mixture is soft and smooth.
Using your hands, pinch off a small amount of dough and shape the melomakarona into a small oval shape, slightly larger than your thumb.
Place the cookies on a baking sheet lined with parchment paper, keeping about ½ inch between them.
Use a fork to create a criss-cross pattern on all the cookies.
Bake in your heated oven for about 25 minutes, until they are crunchy and golden in color.
As soon as you remove the cookies from the oven, soak them in the cold syrup for about 10 seconds, flipping them around.
Remove the cookies from the syrup and arrange them on a tray that is lined with extra crushed walnuts. Drizzle any extra syrup on the cookies.
Sprinkle the cookies with crushed walnuts and you can also add a little dusting of ground cinnamon.