Heat a large sauté pan with a lid over medium heat and add the butter until melted.
Add the chopped onion and minced garlic to the pan and sauté for 2–3 minutes until fragrant and slightly softened.
Season the chicken thighs generously with salt and pepper on both sides.
Push the onions and garlic to the edges of the pan and arrange the chicken in a single layer in the center; brown 1–2 minutes per side until lightly colored, then transfer the chicken to a plate.
Stir the rice, lemon zest, dried rosemary, and chicken bouillon into the pan with the onions and garlic until well combined.
Return the chicken pieces to the top of the rice and pour in 3 cups of water (add more if needed for preferred texture).
Cover, bring to a simmer, then reduce heat and cook gently for 15–20 minutes, until the rice is tender and the liquid is absorbed.
Remove the lid, move the chicken to the side, and stir 1/4 cup lemon juice, the Parmesan, and chopped parsley into the rice; add 1/4–1/2 cup water if the rice needs loosening.
Taste and adjust seasoning with salt and pepper, then serve warm.