Heat the butter or olive oil in a large skillet with a lit. Add the shallot and cook for 2-3 minutes until softened.
Add the rice to the pan and toss to coat in the shallot and butter/olive oil. Cook the rice for 2-3 minutes, stirring often. Add the broth, lemon zest, salt, and pepper, and bring to a simmer.
Cover, reduce the heat to low, and cook for 20 minutes. After 20 minutes, remove the pan from the heat and let it stand covered for another 10 minutes.
Fluff the rice and fold in the lemon juice and fresh dill. Season to taste with additional salt and pepper.