Heat the olive oil in a large soup pot or Dutch oven over medium heat. Add the diced chicken pieces and season them with salt, black pepper, smoked paprika, dried thyme, dried oregano, and crushed red pepper flakes, if using. Sauté until the chicken is fully cooked and lightly browned, approximately 6 to 7 minutes. Remove the chicken from the pot and set it aside on a plate.

In the same pot, add the diced onion, carrots, and celery. Sauté over medium heat until the vegetables become tender, approximately 5 to 6 minutes. Add the minced garlic and continue to sauté for an additional 30 seconds until fragrant.

Sprinkle the all-purpose flour evenly over the sautéed vegetables. Stir constantly for about 1 minute to coat the vegetables and remove any raw flour taste. This process will assist in thickening the soup later.

Gradually pour the chicken broth into the pot, stirring continuously to avoid clumping. Return the cooked chicken to the pot and add the uncooked rice. Incorporate the soy sauce at this stage. Increase the heat slightly and bring the mixture to a gentle boil.

Reduce the heat to low and allow the soup to simmer, uncovered, for approximately 20 to 25 minutes. Stir occasionally to prevent the rice from sticking to the bottom of the pot. If the soup becomes too thick, additional broth may be added as needed.

Stir in the half-and-half and freshly squeezed lemon juice. Simmer for an additional 2 to 3 minutes until heated through. Taste and adjust seasoning with additional salt and pepper, if necessary.

Ladle the soup into serving bowls. Garnish with freshly chopped parsley and, if desired, a sprinkle of additional smoked paprika or freshly ground pepper.