Melt the butter with the shallot in a medium saucepan over medium-low heat. Season with the salt and pepper and cook until the onions are soft, about 5 minutes. Add the rice and stir until coated with the butter. Increase the heat to medium-high. Let the rice cook until toasted, stirring occasionally, about 5 minutes more.
Stir in the broth, bay leaf, and rosemary. Bring to a simmer over low heat, cover, and cook until all the broth has been absorbed by the rice and the rice is tender, about 15 to 18 minutes. Remove from the heat and let set for 5 minutes. Discard the rosemary and bay leaf. Fluff the rice with a fork and serve.
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