Heat olive oil in a large pot or deep skillet over medium heat.
Add the sliced smoked sausage and cook for 5 minutes, stirring occasionally, until browned.
Add the diced onion and cook for 3 minutes until softened.
Stir in the minced garlic and cook for 1 minute until fragrant.
Add the rinsed rice to the pot and stir to coat the rice with the oil and sausage drippings.
Pour in the chicken broth and diced tomatoes with their juices.
Add smoked paprika, dried oregano, black pepper, salt, and crushed red pepper flakes. Stir to combine.
Bring the mixture to a boil, then reduce heat to low and cover the pot with a tight-fitting lid.
Simmer for 18 minutes without lifting the lid.
After 18 minutes, remove the lid and stir in the frozen peas.
Cover again and cook for an additional 5 minutes until the rice is tender and the peas are heated through.
Remove from heat and let the pot sit covered for 5 minutes before serving.