Combine milk, sugar, and butter in a saucepan over low heat and warm to 112 degrees F (44 degrees C). Remove from heat. Stir in yeast and wait for mixture to bubble.
Place flour in a large bowl. Add yeast mixture, whole eggs, egg white, chopped almonds, apricots, orange zest and juice, lemon zest, and mahlepi. Mix together. Knead dough until well mixed, adding extra flour if necessary until dough is only slightly sticky. Set dough aside until doubled in size, about 1 hour.
Combine egg yolk and 1/4 cup milk in a bowl and place in the refrigerator.
Preheat the oven to 350 degrees F (175 degrees C).
Knead risen dough to expel bubbles and divide into 2 equal parts. Divide each half into 3 equal balls. Roll each ball into a rope about 18 inches long. Braid 3 ropes to make a loaf and tuck the ends underneath and place on a baking sheet. Repeat with remaining 3 ropes to form a second loaf. Brush egg yolk mixture on top of each loaf and sprinkle with slivered almonds. Brush again with egg yolk mixture.
Bake in the preheated oven until loaves are brown and sound hollow when tapped on the bottom, about 40 minutes.
