Prepare the chicken: Put the saffron threads in a small bowl and pour the boiling water over them. Let cool, stirring once or twice, then set aside.

Season the chicken pieces generously with salt.

Heat the oil in a large heavy-bottomed skillet or Dutch oven over medium heat. Add the chicken and cook, turning occasionally, until the pieces are nicely browned on all sides, 10-15 minutes. (You may need to do this in batches to avoid crowding the skillet.)

Add the garlic and saffron water to the pan, cover, and adjust the heat to a low simmer. Cook the chicken until it's very tender, almost falling off the bone, 1 to 1 ½ hours. Remove the skillet from the heat and let the chicken cool for about 15 minutes.

Meanwhile, bring a large pot of water to a boil, season well with salt, cover the pot, and then reduce the heat slightly so the water stays hot and almost ready to cook the noodles once the chicken is finished.

In a small bowl, whisk together the egg yolks and lemon juice until well blended.

Pour the egg and lemon mixture into the chicken cooking liquid. Lift the pan and swirl several times until the sauce comes together and is blended.

Return the skillet to low heat and cook gently, swirling the pan or stirring with a silicone spatula, until the sauce reaches 175°F and thickens slightly. You can test for doneness by dipping a large spoon in the sauce and running your finger across the coated spoon; if your finger leaves a clear track that doesn't instantly run back together, the sauce is ready. Taste the sauce and adjust the flavors with more salt and lemon juice if necessary; keep warm while you cook the noodles.

Bring the pot of salted water back to a boil. Add the egg noodles and cook according to the package instructions. Drain well.

Serve the chicken with the egg noodles, ladling the sauce and garlic cloves over the chicken. Sprinkle with parsley, if using.