Place the rice in a fine-mesh strainer and rinse under cold running water until the water runs completely clear to remove excess starch. Let it drain well while you prepare the other ingredients.

In a medium saucepan or pot, melt the unsalted butter with the olive oil over medium heat. Adding the olive oil prevents the butter from browning too quickly and burning.

Add the broken vermicelli pasta to the melted butter mixture. Toast the pasta, stirring constantly, until it turns a deep golden brown and smells fragrant and nutty, about 3 to 4 minutes.

Stir the drained rice into the pot, mixing well to coat every grain with the butter and oil. Sauté the rice for another 2 to 3 minutes until the edges of the grains become slightly translucent.

Carefully pour in the hot broth, then add the salt and black pepper. The mixture will bubble up vigorously, so stir gently to combine everything and bring it to a gentle boil.

Reduce the heat to the lowest setting, cover the pot with a tight-fitting lid, and let it simmer undisturbed for 15 minutes, or until all the liquid is completely absorbed by the rice.

Remove the pot from the heat without opening the lid. Place a clean paper towel or tea towel between the pot and the lid to absorb excess steam, and let the rice rest for 10 minutes. Fluff gently with a fork before serving.