Place the long-grain rice in a fine-mesh strainer and rinse under cold running water until the water runs completely clear, about 1 to 2 minutes. Shake off the excess water and set aside to drain thoroughly.

In a medium saucepan, melt the unsalted butter together with the olive oil over medium heat. Using both oil and butter prevents the milk solids from burning while ensuring a rich, savory flavor.

Add the broken vermicelli pasta to the melted butter and oil mixture. Sauté for 2 to 3 minutes, stirring constantly, until the pasta turns a deep golden brown color and smells distinctly nutty.

Stir in the rinsed and drained rice, cooking it with the toasted vermicelli for another 2 minutes. This step gently toasts the rice grains and coats them in the fat, which helps keep them fluffy and perfectly separated after cooking.

Carefully pour the hot broth into the saucepan, as it may sputter slightly upon contact with the hot pan, and stir in the kosher salt. Bring the liquid to a gentle boil, then immediately reduce the heat to the lowest setting and cover the pan with a tight-fitting lid.

Simmer the rice completely undisturbed for 12 to 15 minutes, or until all of the liquid has been absorbed by the grains. Remove the pan from the heat, place a clean kitchen towel between the pot and the lid, and let it rest for 10 minutes to absorb any excess steam.

Remove the lid and towel, then fluff the rested rice gently with a fork to separate the grains and evenly distribute the vermicelli. Serve hot alongside your favorite Mediterranean-style roasted chicken, kebabs, or a hearty vegetable stew.