Heat olive oil in a large deep skillet or Dutch oven over medium heat.
Add the sliced sausage and cook, stirring occasionally, until browned, about 5 minutes.
Add the diced onion and green bell pepper to the skillet and cook until softened, about 4 minutes.
Stir in the minced garlic and cook for 1 minute until fragrant.
Add the rinsed rice to the skillet and stir to coat with the oil and vegetables.
Pour in the chicken broth and the can of diced tomatoes with their juice.
Add smoked paprika, dried thyme, salt, black pepper, and crushed red pepper flakes. Stir well to combine.
Bring the mixture to a boil, then reduce heat to low and cover the skillet with a tight-fitting lid.
Simmer for 20 minutes without lifting the lid, until the rice is tender and liquid is absorbed.
Remove the skillet from heat and let it sit, covered, for 5 minutes.
Fluff the rice with a fork and stir in the chopped fresh parsley.
Serve hot.