For the syrup:
1. In a saucepan add all the ingredients and heat until the sugar melts.
2. Let cool.
For the mixture of walnut pie:
1. Preheat the oven to 175°C  on the fan.
2. In the mixer's bowl, place the butter and sugar and beat at medium speed with the flat beater.
3. Once the mixture turns white, add the vanilla extract and then one by one the eggs. Then add the milk.
4. In a bowl homogenize all solid ingredients .
5. Then gradually add the solid ingredients to the mixer's bowl.
6. Spread a baking pan with the butter and cocoa powder and then pour the mixture.
7. Bake in the oven for  1 hour.
8. Once it is cooked, syrup.