Rinse the fresh quince and pat dry. Peel quarter and core each one. Grate the quince quarters into a bowl.
Add the apple juice and toss together to coat completely. Let stand for 15 minutes.
Place the all-purpose flour in a large bowl and make an impression in the middle.
Pour the active dry yeast into the well, sprinkle 1/2 the white granulated sugar over the yeast, and pour 1/2 the lukewarm milk over the sugar and yeast.
Cover and stow in a warm place for 15 minutes.
Roughly chop the almond splinters.
Grease a large (9×14) loaf pan.
Retrieve the bowl of yeasted dry ingredients from its warm place.
Mix the contents of the bowl together with the grated fresh quince, salt, egg, melted unsalted butter, the rest of the white granulated sugar, and lukewarm milk.
Place the mixture back in the bowl, cover, and let stand for another 30 minutes or until the dough has doubled in size.
Preheat the oven to 350 degrees F.
Turn the dough out onto a lightly floured surface and knead once more.
Transfer the dough to the greased loaf pan.
Place in the oven and bake for 45 minutes.
Remove from oven. Cool, then slice and serve while the bread is still warm.