Melt the butter in a medium heavy-bottomed saucepan over medium heat. Add the vermicelli and stir constantly until deep golden brown, about 3 to 4 minutes.

Add the rice and cook, stirring, for 1 to 2 minutes until the grains turn translucent around the edges and smell toasty.

Pour in the broth, add the salt and bay leaf, and bring to a boil. Reduce the heat to low, cover tightly, and simmer for 15 minutes without lifting the lid.

Remove the pot from the heat and let it rest, covered, for 5 minutes. Discard the bay leaf, fluff the pilaf with a fork, and serve in a warm bowl topped with parsley.