Prepare the yeast starter. Place the sugar and milk into a saucepan and heat just until warm. Remove from the heat and add the crushed yeast. Pour the milk mixture over the flour and mix to combine. Cover the bowl with plastic wrap and let the dough rise until it increases in volume, about 15 minutes.
Prepare the dough. Combine the yolks, the 2 whole eggs, salt and sugar and mix until foamy and light yellow.
Add Greek yogurt, orange and lemon zest and vanilla and mix to combine, then add the sifted flour. Start kneading the dough until smooth. Then add alternately, the oil and butter (about 5 tranches) and continue kneading by folding the dough, until it pulls away from the sides of the bowl. Finally hit it a few times, throw it in the bowl in which we kneaded it, then transfer the dough into an oiled greased bowl. Cover with plastic wrap and refrigerate for 14 hours.
Prepare cocoa filling. Mix eggs with salt, sugar and citrus zest until foamy and the sugar is dissolved. Add rum essence or extract if desired. Add cocoa, ground walnuts or pecans and mix with a spatula. Divide mixture in four.
Preheat the oven to 400°F (200°C). Grease with oil the bottom and sides of two 12 x4.4 inches (30x11cm) loaf pans and line with parchment paper.
Divide the dough into four equal parts. Onto a floured surface, roll each part into a 8×12 (20x30cm) rectangle. Spread ¼ of cocoa filling over the rolled dough, and spread 1/3 cup (100g) Nutella over the cocoa filling.
Roll up the dough, and repeat with the remaining dough and filling.
Braid 2 of the rolled pieces starting from the middle and pinch the ends. Place in the prepared loaf pan. Repeat with the remaining 2 pieces of rolled dough.
Cover with a kitchen towel and leave to rise at room temperature until it doubles in volume for about 45 minutes or more depending on the room temperature.
Brush with beaten egg before baking.
Bake at 400°F (200°C) for 9 minutes, then reduce the oven temperature to 320°F (160°C) and bake for another 45 minutes.
Let it cool slightly before serving. If desired, top with chocolate glaze.
Prepare chocolate glaze. Add all ingredients into a heat proof bowl and place over a pan with simmering water until the chocolate melts.
Strain and pour over the babka. Enjoy!