Warm the milk until just lukewarm, then stir in the yeast and a teaspoon of sugar. Leave for 5 to 10 minutes until frothy. This stage ensures the yeast is active and gives the dough its characteristic airy texture before moving to the next step.
In a large bowl, combine the flour, remaining sugar, and salt. Add the yeast mixture, egg yolks, melted butter, and vanilla extract. Mix until a soft dough forms, then knead for about 8 minutes until smooth and elastic. The dough should feel supple rather than sticky before continuing.
Place the dough in a lightly greased bowl and cover with a clean tea towel. Leave in a warm place for 1 to 1½ hours until doubled in size. A slow rise develops flavour and gives the dumplings their delicate crumb.
In a shallow bowl, mix the ground walnuts, caster sugar, and cinnamon. Melt the butter in a separate bowl. These layers create the nutty sweetness that defines traditional Aranygaluska before assembling the dumplings.
Punch down the risen dough gently and roll it to roughly 2 cm thickness on a lightly floured surface. Cut small rounds using a pastry cutter or glass. Keep the pieces similar in size for even baking as you move to coating them.
Dip each dough piece into melted butter, then roll in the walnut mixture. Arrange the coated pieces loosely in a buttered baking dish, layering them slightly so they bake together while still pulling apart easily. Continue until all dough is used.
Cover the dish loosely and allow the dumplings to rise again for 30 minutes. This final proof creates a lighter texture and helps the layers expand beautifully in the oven before baking.
Preheat the oven to 180°C fan. Bake for 30 to 35 minutes until deeply golden on top and fragrant. The sugar and butter will caramelise around the edges, creating crisp pockets between the soft dumplings.
While the dumplings bake, heat the milk gently in a saucepan. In a bowl, whisk egg yolks, sugar, and vanilla extract. Slowly pour in the warm milk while whisking, then return to low heat and stir until slightly thickened. Avoid boiling to keep the sauce silky and smooth.
Allow the Aranygaluska to cool for 10 minutes before serving warm. Spoon over the vanilla sauce and scatter extra walnuts on top if desired. Serve fresh from the baking dish so everyone can pull apart the golden dumplings at the table.