Place the long-grain rice in a fine-mesh strainer and rinse under cold running water until the water runs completely clear. Drain the rice thoroughly and set aside.

In a medium saucepan with a tight-fitting lid, heat the olive oil and unsalted butter over medium heat until the butter is completely melted and slightly foamy.

Add the broken vermicelli pasta to the saucepan and toast, stirring constantly, until it turns a deep, nutty golden brown, about 3 to 4 minutes. Watch closely as the pasta can burn very quickly.

Add the rinsed, drained rice to the pot and stir continuously to coat the grains in the butter mixture. Toast the rice for 2 to 3 minutes until the edges of the grains become slightly translucent.

Carefully pour the hot broth into the saucepan, being cautious as the liquid will sputter. Stir in the kosher salt and black pepper, and bring the mixture to a gentle boil.

Reduce the heat to the lowest possible setting, cover the pot tightly with the lid, and let it simmer undisturbed for 15 minutes, or until all the liquid is absorbed.

Remove the pot from the heat. Take off the lid, place a clean kitchen towel or a double layer of paper towels over the pot, and replace the lid tightly. Let the rice rest for 10 minutes to absorb any excess moisture.

Gently fluff the rested rice with a fork, ensuring the vermicelli is evenly distributed. Serve hot alongside your favorite roasted meats, grilled chicken, or rich stews.