Rinse the rice in a fine-mesh strainer under cool water until it runs mostly clear. Shake off excess water and let it drain for a few minutes while you prep the aromatics.
Melt the butter with the olive oil in a medium saucepan over medium heat. Add the minced garlic and cook just until fragrant, about 30 seconds.
Stir in the drained rice along with the turmeric and black pepper. Toast, stirring often, until the grains look slightly translucent at the edges and smell nutty, 2 to 3 minutes.
Pour in the broth, then add the salt, lemon zest, and bay leaf. Give it one good stir, bring to a lively simmer, and then reduce the heat to low. Cover tightly.
Cook covered on low until the liquid is absorbed and small steam holes appear on the surface, 15 to 17 minutes. Avoid lifting the lid during this time.
Remove from the heat and let the rice rest, still covered, for 5 minutes to finish steaming. Discard the bay leaf.
Drizzle in the lemon juice and fluff gently with a fork. Fold in the fresh dill or parsley, taste, and adjust with a pinch more salt or lemon if you like. Serve warm.