Pay attention! This has a number of unusual steps.

1. Mix the fresh yeast with 1 cup of the sugar. This will go easier than you expect.
2. Pound the mastic to a powder and mix half a teaspoon of the crushed mastic with the other cup of sugar. Save the other half of the mastic for the end of the recipe
3. Warm the milk with the sugar-mastic mixture to dissolve the sugar.
4. Let the milk mixture cool a bit. Beat the eggs and add them to the milk mixture.
5. Add the warm milk-egg mixture to the yeast mixture in a big bowl.
6. Sprinkle all of the Mahleb on top and let the mixture proof until it is foamy.
7. Add the flour cup by cup and mix well.
8. Knead the dough vigorously until it is very smooth and elastic.
9. Spread the dough out and dot it with the soft butter, then fold over the dough again and again, working the soft butter into it patiently until it is all incorporated.
10. Let the dough rise in a warm place until doubled in bulk. This won't happen in a cold room; consider warming the oven a little and then let the dough rise in there, covered.
11. Preheat the oven to 375. Flour two baking sheets. One can be medium, but the other should be pretty big.
12. Divide the dough in half, and then divide one half into a third and a 2/3 piece. The 2/3 piece will become the smaller, simpler loaf. The big half and the small third together make up the traditional big Easter loaf.
13. Form the 2/3 piece into a loose spiral on a floured board and set one red egg in the center. Make a loose spiral to allow the dough to rise.
14. For the big traditional braided loaf, press the big half into a flattened roll a little longer than the small roll, and slice it most of the way up the middle, then spread the legs to make a sort of U. Set the small strip between the legs (I am not trying to be erotic here...). You should have a big U with a small i inside. Now braid the three strands loosely and set the other red egg in the space between the top of the i and the bend in the U.
15. Somehow you will have to get this on a baking sheet. I find it easier to braid it first, then slide the floured baking sheet under the braided loaf.
16. Brush the loaves with milk and sprinkle with the remaining mastic gum.
17. Allow the loaves to rise as much as they want to - an hour or longer.
18. Bake in the preheated oven for 40-50 minutes. You will be able to smell when it is nearly done.
19. Cool completely on a rack before cutting.