For the dough: Combine the egg, butter, sour cream, chives and 1 teaspoon salt with your hands in a bowl. Don't worry if the mixture is not uniform and, as with pie dough, don't overwork it. Add the flour and mix with your hands until a dough forms. Wrap in plastic and refrigerate the dough at least 2 hours and up to 2 days.
Roll the dough into 1/2-inch-thick ropes and cut into dumplings.
Bring a large pot of water to a boil and salt liberally. Drop in the dumplings and cook until they float to the top, about 2 minutes.
For the roast and veggies: Meanwhile, add the butter to a large pan over medium heat and begin to brown for 2 minutes. Add the chicken and spinach and toss to combine. Cook to warm the chicken and begin to wilt the spinach, about 2 minutes. Add the rosemary and cook for 2 more minutes.
Add 1/2 cup of the dumpling cooking water and the dumplings and simmer until the flavors come together. Remove from the heat, toss in the Parmesan and serve.
For more ingredient substitution ideas, see the article below.