In a bowl add the olive oil, the plant butter (not melted) and the sugar, while stirring with a whisk. Dissolve the soda in the orange juice and add it to the mixture. Add the cognac. In a bowl, mix the flour, baking powder, cinnamon, cloves, ground almonds and ground walnut pieces (note that the nuts must be coarsely-chopped. If they become powdery, we must remove some flour). Mix them and add them to the butter mixture. Mix gently. Let the dough rest for 15 minutes. Take a small ball of dough, the size of a walnut, 35-40g approximately, knead it slightly giving it an oval shape. Place the Melomakarona in a pan covered with non-stick baking paper and press them lightly. If you want the Melomakarona to absorb more syrup, pierce them with a fork. Bake them at 180° C, on the top and bottom resistors and fan for 25-30 minutes. Let them cool down. If you wish, you can fill the Melomakarona with dates and walnut pieces. Remove the pit from the date and replace it with half a walnut. Press the Melomakarona dough to open into a pie and place the date with the walnut in the middle. Close carefully and bake normally in the oven.
For the coating: In a bowl, mix the walnut and almond pieces.

For the syrup: Put all the ingredients in a pot and when they boil, simmer for 5-6 minutes and skim off the syrup. Next, add the lemon and leave the syrup on the lowest heat. Put the Melomakarona in the syrup and press them with a ladle. Leave them in the syrup for about 2 minutes on each side. Take the Melomakarona out on a grill and sprinkle them with the walnut and almond pieces.