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First, prepare the quick chicken stock. Mix together all ingredients in a medium-sized saucepot over medium-high heat until the mixture begins to boil. Cover, reduce heat to low, and allow to simmer for 1 hour.
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About 30 minutes in to the simmering time, you can start preparing the braised chicken with hot Hungarian paprika. Cook the bacon and onion together in a large skillet over medium heat until the onions are lightly golden around the edges and the bacon is crispy. Remove the bacon and onions from the pan and set them aside, leaving the remaining juices in the skillet.
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In a flat bowl, mix together the flour, salt, 1 teaspoon of the hot Hungarian paprika, and 1/2 teaspoon of the regular paprika. Place each piece of chicken in the bowl and lightly coat with the flour mixture. Place the chicken pieces in the skillet and cook until lightly browned on each side. Add 2 tablespoons of the quick chicken stock to the skillet, cover, and bring the heat dow to low. Simmer for 45 minutes.
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Meanwhile, you can begin making the paprika sauce. Melt the butter over medium heat and whisk in the flour until a paste forms. Add 1 cup of the quick chicken stock and whisk until completely combined. Bring the mixture to a rapid boil and allow to cook for 4 minutes. Slowly add the milk to the sauce, followed by the remaining tablespoon hot paprika and 2 teaspoons normal paprika, whisking constantly until combined. Once the mixture is hot but not boiling, remove it from heat and whisk in the sour cream and then the reserved bacon and onion bits. The sauce should now be very thick.
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Pour the sauce over the chicken in the pot and allow to simmer for 8 minutes, uncovered. Then remove from heat, cover, and set aside.
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To prepare the spatzle, bring a large pot of water to a boil. Mix together the flour, parsley, and salt in a medium-sized bowl and set aside. In a small bow, whisk together the egg and 1 cup water until well-blended. Pour the egg mixture into the flour mixture and stir until a thick dough forms. Drop the dough into the boiling water in even 1/2 teaspoon-fulls.
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Once they rise to the top of the water, cook them for an additional 5-8 minutes, or until they are soft (not stiff) when you press them against the side of the pot with a fork. Remove with a slotted spoon, shake off excess water, and place them in a bowl as they finish. Toss them with the olive oil and then lay them out on a serving platter. Top with the chicken and sauce and serve immediately.