Christmas log with chestnut cream

INGREDIANTS 5 large whole eggs 130 grams of sugar 120 grams of flour 30 gr of oil 1 vanillin sachet 1 pinch of salt For the filling 400/450 gr of chestnut cream (chestnut jam) 250 grams of mascarpone 1 teaspoon of unsweetened cocoa For the "bark" 100/110 gr of milk (or dark) chocolate