Heat the olive oil in a large pot over medium heat.
Add the diced onion and cook for 3-4 minutes until translucent.
Add the minced garlic, diced carrot, and diced red bell pepper. Cook for another 5 minutes, stirring occasionally.
Stir in the diced tomato, smoked paprika, ground cumin, dried thyme, cayenne pepper, salt, and black pepper. Cook for 2 minutes to combine the flavors.
Add the rinsed rice to the pot and stir well to coat the rice with the spices and vegetables.
Pour in the vegetable broth and bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 20 minutes.
After 20 minutes, add the frozen peas, stir gently, and cover again. Cook for an additional 5-10 minutes until the rice is tender and the liquid is absorbed.
Remove the pot from heat and let it sit, covered, for 5 minutes.
Fluff the rice stew with a fork and stir in the chopped fresh parsley before serving.