DUMPLINGS:

1 1/2 tsp. active dry yeast (1/2 env.)
2 tbsp. sugar
1/4 c. lukewarm water (110-115 degrees)
3/4 c. lukewarm milk (110-115 degrees)
2 tbsp. butter, melted
1/4 tsp. salt
3/4 c. sifted all-purpose flour

POACHING LIQUID:

2 tbsp. butter
2 tbsp. sugar
1/2 c. cold milk

In a small, shallow bowl, sprinkle the yeast and 1 tablespoon of the sugar over the 1/4 cup of lukewarm water. Let the mixture stand for 2 or 3 minutes, then stir it to dissolve the yeast. Set the bowl in a warm, draft-free place - such as a turned-off oven - for 4 or 5 minutes, or until the yeast bubbles and doubles in volume.

In a mixing bowl, combine the lukewarm milk, melted butter, the remaining 1 tablespoon of sugar, and 1/4 teaspoon of salt. Add the yeast and then the flour, beating until a smooth dough is formed. Gather the dough into a ball and knead it vigorously on a lightly floured surface for about 5 minutes, or until it is smooth and elastic. Then return the dough to the bowl, dust it lightly with flour, and cover with a kitchen towel.

Set the dough in a warm, draft-free place for about 45 minutes, or until it has doubled in bulk. Punch the dough down with one blow of your fist. Divide the dough into 10 or 12 equal pieces and with lightly floured hands shape them into balls.

Place them 2 inches apart on a baking sheet and set them aside in the same warm place to double in bulk again. Then, in a heavy 10-inch skillet 2 1/2 inches deep or a flameproof casserole of similar size, melt 2 tablespoons of butter over moderate heat. When the foam subsides, stir in 2 tablespoons of sugar and 1/2 cup of cold milk.

Bring to a boil, then arrange the dumplings side by side in the skillet and cover it tightly. Reduce the heat to low and simmer undisturbed for 15 minutes, or until the dumplings have absorbed all the liquid. Remove from the heat and set the dumplings aside in the covered skillet to keep them warm.

VANILLA SAUCE:

4 egg yolks, lightly beaten
1/2 c. sugar
2 c. cold milk
1 tsp. vanilla extract

While the dumplings are poaching, make the vanilla sauce. Beat the egg yolks and sugar together with a wire whisk or a rotary or electric beater for 3 or 4 minutes, or until the yolks are thick and pale yellow. Bring 2 cups of cold milk to a boil in a heavy 2 to 3-quart saucepan and then, beating constantly with a whisk, pour the milk in a thin stream over the yolks. Pour the mixture back into the saucepan and cook over low heat, stirring constantly with a spoon, until the sauce is thick enough to coat the spoon lightly. Do not let the sauce come to a boil or it may curdle. Remove the pan from the heat and stir in the vanilla.

To serve, arrange the dumplings, bottom sides up, on a heated platter or individual serving plates and spoon the vanilla sauce over them.