Place the rice in a fine-mesh strainer and rinse under cold running water until the water runs completely clear. Shake off as much excess water as possible to ensure the grains will fry properly and not become mushy.

In a medium saucepan with a tight-fitting lid, heat the butter and olive oil over medium heat until the butter is completely melted and foamy. Add the broken vermicelli pasta and toast it, stirring constantly, until it turns a deep golden brown, about 2 to 3 minutes.

Add the drained rice to the saucepan with the toasted vermicelli. Sauté the mixture, stirring frequently, for 2 to 3 minutes until the rice grains begin to look slightly translucent at the edges, which helps lock in their shape.

Carefully pour the hot broth into the saucepan—be cautious as it will bubble up vigorously—and stir in the salt and black pepper. Bring the liquid to a gentle simmer, then immediately reduce the heat to the lowest setting and cover the pan with the lid.

Simmer the rice undisturbed for 15 minutes, or until all the liquid is absorbed. Do not lift the lid during this cooking process.

Remove the saucepan from the heat, keeping the lid on, and let the rice rest for 10 minutes to allow the steam to finish fluffing the grains. Remove the lid, fluff the rice gently with a fork to separate the grains, and serve warm alongside your favorite main course.