Heat the vegetable oil over medium heat in a large pot or dutch oven. While that is heating sprinkle the cut chicken with kosher salt. fresh ground black pepper, and smoked paprika. Add the chicken to the hot pot and brown on both sides until cooked through. Plate the chicken and cover it to keep it warm.
Melt the butter in the pot over medium heat. Add the onions, celery, and carrots. Cook until the onions and celery are soft stirring several times.
Reduce the heat to low and add the garlic cooking for about 30 seconds while stirring constantly. Stir in the flour and continue cooking for a couple of minutes while stirring.
Stir in the wild rice, chicken broth, and bay leaves. Bring the mixture to a low boil then cover and reduce to a simmer. Simmer for about 40 minutes or until the rice is tender.
Add the cooked chicken back to the pot and simmer for a few minutes. Remove the pot from the heat and stir in the cream, thyme, and rosemary. Ladle into bowls and garnish with more fresh thyme or rosemary.