Heat 3 tbsp olive oil in a large, heavy-bottomed pot or Dutch oven over medium heat. Add 1 small yellow onion, diced and ½ green bell pepper, diced and cook until softened, about 5 minutes. Add 4 garlic cloves, minced and cook 1 more minute until fragrant.
Add 2 cup long-grain white rice to the pot and stir to coat in the oil. Toast for 2 minutes, stirring frequently. Stir in 2 tbsp tomato paste, 1 tsp ground turmeric, ½ tsp ground cumin, and ½ tsp smoked paprika, then add ½ tsp smoked paprika and cook 30 seconds.
Stir in 2 tbsp tomato paste until incorporated. Pour in 3 ½ cup chicken broth and add 1 bay leaf, ¾ tsp salt, and ¼ tsp black pepper. Bring to a boil over medium-high heat.
Once boiling, reduce heat to low, cover tightly, and cook until rice has absorbed all the liquid.
Remove from heat. Discard the bay leaf. Gently fold in ½ cup green olives, sliced (manzanilla or Castelvetrano) and 2 tbsp capers, drained. Replace the lid and let the rice steam off the heat for 5 minutes.
Fluff the rice with a fork, taste and adjust salt if needed, and garnish with 2 tbsp fresh cilantro or parsley, chopped (for garnish). Serve warm.