Bring a large stockpot of salted water to a boil (it should taste like sea water).
Meanwhile, heat the oil over medium-high heat in a large, straight-sided saute pan until it shimmers. Sprinkle the chicken livers liberally with salt and pepper. In two batches, add the chicken livers to the hot oil and brown on both sides, about 3 minutes per batch. Transfer the browned livers to a plate.
Once all of the livers have been browned, add 2 tablespoons of the butter to the pan. Add the mushrooms and cook until lightly browned, about 5 minutes, stirring occasionally. Add 2 more tablespoons of the butter and the onions, season with salt and pepper and cook until slightly softened and lightly browned, 3 to 5 minutes. Take the pan off of the heat and carefully add the cognac. Stir to combine, place the pan back on the heat and cook for 1 minute, stirring constantly. Add the chicken broth and cook until reduced by half, 3 to 5 minutes.
Meanwhile, slice the browned livers into long strips about 1/2-inch thick.
Reduce the heat to medium-low, stir the yogurt into the sauce and season with salt and pepper. Then add the livers and stir to combine. Simmer the sauce until the livers are cooked to your liking, 3 to 5 minutes for medium. Season with salt and pepper.
While the livers are cooking in the sauce, cook the egg noodles in the boiling water until al dente, 5 to 8 minutes. Then drain. Toss the hot egg noodles with the remaining butter and half of the parsley. Season with salt and pepper.
To serve, divide the egg noodles among 4 to 6 bowls and top with the chicken livers and sauce. Garnish with the remaining parsley. Alternatively, this dish can be served family-style on a large platter.