Bring a large pot of salted water to a boil. Cook the egg noodles according to the package instructions until just tender. Drain and set aside.
While the noodles cook, heat the olive oil in a large, deep skillet or Dutch oven over medium heat.
Add the chopped onion and cook for 3 to 4 minutes, stirring occasionally, until it begins to soften.
Add the chicken thighs. Season with the smoked paprika, onion powder, black pepper and a small amount of salt. Cook for 5 to 7 minutes, stirring occasionally, until the chicken is lightly browned on the outside.
Add the sliced carrot and drained green beans. Cook everything together for another 3 to 4 minutes.
Pour in the chicken broth and stir. Bring to a gentle simmer and cook for approximately 8 to 10 minutes, or until the chicken is completely cooked and the carrots are tender.
Reduce the heat and stir in the cream. Let the sauce heat gently without bringing it to a rapid boil.
Meanwhile, prepare the roux. Melt the salted butter in a small saucepan over medium-low heat. Add the flour and whisk continuously for 1 to 2 minutes, until the mixture is smooth and no longer smells like raw flour.
Gradually add a few spoonfuls of the warm cooking liquid to the roux, whisking after each addition. Once the mixture is smooth and pourable, add it to the chicken and vegetables.
Stir well and let the sauce simmer gently for 2 to 3 minutes, until it thickens enough to coat the back of a spoon.
Add the cooked egg noodles and gently stir until they are evenly coated. If the sauce becomes too thick, add a small splash of chicken broth.
Taste and adjust the salt and pepper before serving.
