In a bowl, mix the lard well with the powdered sugar and vanilla sugar until it becomes frothy. Add the egg and mix again. Add sour cream, grated lemon peel and vinegar. At the end, add flour mixed with baking powder. Mix then turn over on the work table and knead lightly until you get a homogeneous dough that can be stretched. Let cool for 2 hours.
Put the plum jam in a bowl and mix it with ground walnuts, so as to obtain a fairly thick composition. Add the rum essence to taste.
Remove the dough from the refrigerator and break pieces of it that are spread on the floured work table in a circle. Then cut the circle into 8 equal triangles. Place a teaspoon of walnut jam composite on the outer edge and then roll inwards, forming the croissant. Lightly press the corners and bend in the shape of a crescent.
Place in the pan and place in the preheated oven at 180 degrees for about 30-35 minutes or until lightly browned.
Sprinkle vanilla powdered sugar on top and serve.