Melt the butter and beat until frothy. Gradually stir in the sugar and vanilla sugar. Add the eggs, lemon juice and lemon zest. Mix well. Stir in the flour. Quickly stir into a smooth dough, cover and let rest for about 3 hours.
Divide the dough into fourths. Roll each piece onto a floured surface into a 1.5 cm thick roll. Cut each roll into 1.5 cm long pieces.
Heat the clarified butter in a deep fryer to 170°C (approximately 350°F). Fry the dough pieces in the butter for a few minutes, turning occasionally. Drain on paper towels. Serve dusted with powdered sugar.