Warm the olive oil in a medium-sized Dutch oven or pot over medium heat. Add the diced onion and sauté for 5 to 8 minutes until it becomes soft and translucent. Incorporate the rinsed rice and toast it for about 2 minutes, stirring frequently, until it releases a nutty aroma.
Mix in the tomato paste and minced garlic, ensuring they are evenly distributed. Next, add the diced fresh tomatoes or tomato sauce, chopped jalapeño, sea salt, oregano, and vegetable broth. Increase the heat to bring the mixture to a boil.
Once boiling, reduce the heat to low, cover the pot with a tight-fitting lid, and let it simmer gently for 15 minutes, or until the liquid has been absorbed and the rice is tender.
Remove the pot from the heat but keep it covered. Allow the rice to rest for an additional 10 minutes to finish steaming. Before serving, fluff the rice with a fork to separate the grains and enjoy this flavorful, aromatic Spanish rice.