Heat the olive oil in a large deep skillet over medium-high heat. Add the kielbasa slices in a single layer and cook for 4-5 minutes, turning once, until both sides are nicely browned and the fat starts to render. Transfer to a plate and set aside.

Reduce heat to medium. Add the onion and bell pepper to the drippings in the pan. Saute for 5-6 minutes, stirring occasionally, until the onion turns translucent and the edges start to brown. Add the garlic, smoked paprika, thyme, and black pepper; cook for 30 seconds until fragrant.

Stir in the rice and cook for 1 minute to toast slightly. Pour in the chicken broth and return the kielbasa to the pan, nestling it into the rice. Bring to a boil, then immediately reduce heat to low, cover tightly, and simmer for 18-20 minutes. Do not lift the lid. The rice is done when all liquid is absorbed and the grains are tender.

Remove from heat and let stand, covered, for 5 minutes. Fluff the rice with a fork, taste for seasoning (the kielbasa adds salt, so you likely won't need more), and sprinkle with fresh parsley before serving.