Heat the olive oil in a large pan or pot over medium heat. Add the chicken pieces and brown them lightly for 2 to 3 minutes per side. The chicken does not need to be fully cooked at this point.
Add the onion, carrot, bay leaves, salt, black pepper, and water or chicken broth. Bring to a gentle simmer, then cover and cook for 35 to 40 minutes, or until the chicken is tender and cooked through.
Remove the chicken from the pan and set it aside. Strain the cooking broth and keep it warm. Measure out 3 cups of warm broth for the creamy sauce.
In a clean pan, melt the butter over medium-low heat. Add the flour and whisk for 1 to 2 minutes, until smooth and lightly bubbly.
Slowly pour in the warm chicken broth while whisking constantly. Keep whisking until the sauce becomes smooth, creamy, and slightly thickened.
In a small bowl, mix the sour cream with a few spoonfuls of warm chicken broth or warm sauce until smooth. Stir the sour cream mixture into the pan and keep the heat low.
Add the minced garlic, salt, and black pepper. Stir well and let the sauce warm gently. Do not boil the sauce after adding the sour cream.
Return the chicken to the pan and spoon the creamy sauce over the top. Cover and simmer gently for 5 to 8 minutes, until the chicken is warm and coated in the sauce.
Stir in the fresh dill at the end. Serve warm with mashed potatoes, rice, bread, or anything that can soak up the sauce.