Place a large stockpot or dutch oven over medium heat.
Pour in oil.
When oil is hot and shimmering, add onion, celery, carrots, garlic and thyme. Cook for about 7 to 10 minutes, until tender and fragrant.
Add 3 quarts of water.
Season with salt and pepper, to taste.
Add chicken. Increase heat slightly and bring to a simmer. Continue simmering for 25 to 35 minutes, or until the chicken is cooked through to an internal temperature of at least 165°F.
Remove chicken from the pot while the broth continues to simmer.
Pull all of the meat off the bones. Discard bones.
Return the meat to the pot.
Add 3 cups cold water to a large bowl. Add bread and soak for 1 minute.
Remove bread, squeezing as much water out as possible.
In a separate medium bowl, add eggs, paprika and salt and pepper, to taste. Mix.
Add soaked bread and work into egg mixture until if forms a dough.
Skim the fat off of the top of the broth with a spoon.
Add the dumpling dough, one spoonful at a time, into the simmering soup. Cook 2 to 3 minutes, or until the dumplings float.
Taste. Add more salt and pepper, to taste, if needed.
Place in a serving bowl or individual bowls and sprinkle with paprika.
Serve hot.