Mix the flour and 1 tsp salt in a large bowl. Add the 90 ml olive oil and 160 ml lukewarm water, stir until it comes together, then knead on the counter for 5 minutes until the dough is soft and smooth. If it sticks to your hands, add 1 tbsp flour at a time. Cover and leave at room temperature for at least 30 minutes while the meat simmers.

Put the beef, quartered onion, bay leaf and 1 tsp salt in the 5-quart / 4.7 L pot and add the 1.5 L water. Bring to a boil over high heat and skim off the foam for the first 5 minutes. Lower the heat to a gentle simmer, set the lid slightly open, and cook for 45 minutes.

Add the chicken thighs and simmer for 30 more minutes, until the beef is tender when pierced with a fork and the chicken pulls easily from the bone. Lift the meat onto a board and strain the broth through a fine-mesh sieve. Measure out 400 ml of broth and save the rest for soup. Let the meat cool while you cook the rice.

Heat the 3 tbsp olive oil in the 3-quart / 2.8 L saucepan over medium heat. Cook the chopped onion for 6 to 7 minutes, until soft and lightly golden. Stir in the rice for 1 minute, then add 300 ml of hot broth. Bring to a simmer, cover, and cook on low for 12 minutes, until the liquid is absorbed and the rice is almost tender with a slight bite. Tip it into a large bowl.

Discard the chicken bones and shred the chicken. Pull or chop the beef into pieces about 1 cm. Add all the meat to the rice with the parsley, kefalotyri, nutmeg, pepper and 1/2 tsp salt, then stir in 100 ml of broth. Taste and add more salt if needed. Let the mixture cool for 10 minutes, then stir in the 2 beaten eggs.

Press a spoonful of filling in your hand. It should hold together without dripping. If liquid pools in the bowl, leave it behind when you fill the pie.

Heat the oven to 190 C / 375 F with a rack in the lower third. Brush the 23 x 33 cm / 9 x 13-inch baking dish with 1 tbsp olive oil. Cut the dough into two pieces, one about two-thirds and one about one-third. Roll the larger piece on a floured counter to about 3 mm thick and line the dish, letting it hang over the edges by about 2 cm.

Spoon in the filling and press it level with the back of a spoon. Roll the smaller piece of dough to a rectangle slightly larger than the dish and lay it on top. Fold the overhang over the lid and press the edges with a fork to seal. Prick the top all over with a fork and brush with the egg yolk mixed with 1 tsp water.

Bake for 45 minutes, until the top is deep golden and the edges are crisp. Rest the pie in the dish on a rack for 15 minutes, then cut into 12 squares.