Preheat oven to 350°F. Grease two 8½- x 4½-inch loaf pans with cooking spray or oil. 

Dough:

Mix yeast and sugar in a large bowl. Add warm water, cover with a towel or plastic wrap and rest in a warm place for 30 minutes, until the surface is spongy and the yeast bubbly.

Add flour, oil, salt, yolks, and eggs to the dough sponge. Combine all ingredients and knead well. Transfer dough to a lightly greased bowl. Cover and rise for 2 hours.

Filling:

In a small bowl, mix sugar and cinnamon. Set aside.

Shaping and Baking:

Divide dough in half. With a rolling pin, roll one dough half into a 16-inch square. Drizzle evoo on dough, then sprinkle with sugar-cinnamon mixture. Spoon and spread half of the apple pie filling on dough.

Roll the dough tightly into a rope, being sure to seal the ends. Slice the rope lengthwise and wrap the halves around each other at least 6 times. Fold the rope in half and place in greased loaf pan. Repeat with remaining dough. Let babkas rise for 45 minutes.

Bake at 350°F for 30 minutes, until golden brown. 

Caramel Glaze:

In a small bowl, combine both sugars, evoo, and almond or soy milk. Drizzle glaze on cooled babka, slice, and serve.