Preheat oven at 350 degrees F.
In a large bowl mix the olive oil, cognac or brandy, orange juice, sugar, 1 tsp cinnamon, ground clove and orange peel.
In another bowl sift flour and mix with the baking powder and baking soda. Add the flour gradually to the olive oil mixture, while stirring with a wooden spoon. Do not add all of it at once, stir with the spoon and add flour until you have soft and shiny dough, it should not be dry. Knead the dough just a bit until it comes together. Do not over knead. Let it rest for 20 minutes.
Roll the dough in little balls about the size of a walnut. Using your fingers press one side of the ball on a grater flattening like a small pancake or pierce with a fork and then fold over so that the cookie is in a oval shape, with the top having the design of the grater. This is done so that the honey will be better absorbed as opposed to just shaping the cookie in a solid oval shape.
Place the cookies on a cookie sheet lined with parchment paper or aluminum foil. Bake for about 25-28 minutes. Bake the rest of the cookies.
Once all the cookies are baked, transfer to large casserole dish and flip them so that the bottom part is facing up, let them cool down completely.
For the syrup bring to a boil the honey, syrup, water, cinnamon stick and slice of lemon and let it boil for 5 minutes. Remove the foam.
Once the syrup is boiled, while it is hot, pour it over the cold cookies, making sure all cookies are covered with syrup. Let the cookies sit for at least 2-3 hours with the top side facing down so that they absorb the syrup * (Some people prefer to do the opposite: Make the syrup and let it cool off, than pour the syrup over hot cookies, instead of letting them cool down. Another way is to place the melomakarona in the pot with the syrup for a few minutes and removing them with a slotted spoon.)
Mix the walnuts with cinnamon turn over on the melomakarona right side again, sprinkle over the melomakarona.
Place the melomakarona on a large platter.