Preheat the oven to 350°F (175°C) and place the oven rack in the middle position.
Season both sides of the chicken thighs with salt and pepper.
Heat the cast iron or ovenproof skillet over high heat and add the oil.
When the oil is hot, sear the chicken thighs (skin side down if using skin-on) until browned, about 4–5 minutes per side; transfer the browned chicken to a plate.
Lower the heat to medium, add the minced garlic to the same pan, and cook, stirring, for about 1 minute until fragrant.
Add 1/4 cup water, soy sauce, lemon juice, honey, and optional minced ginger to the pan; simmer over medium heat, stirring occasionally, until the sauce reduces and slightly thickens, about 5–8 minutes.
If a thicker sauce is desired, whisk together 2 tablespoons cornstarch and 3 tablespoons water, then stir the slurry into the sauce and cook until thickened. Transfer the finished sauce to a bowl and set aside.
Reduce heat to low–medium and add the butter to the skillet. Once melted, add the diced onion and cook, stirring, for about 1 minute.
Add the dry basmati rice, dried rosemary, and lemon zest to the pan; stir and cook for 1 minute to coat the rice in butter and aromatics.
Pour in the 2 cups of low-sodium chicken broth and stir to combine, scraping any browned bits from the pan into the rice mixture.
Return the seared chicken thighs to the skillet, placing them on top of the rice (skin side up if using skin-on thighs).
Cover the skillet tightly with foil and bake in the preheated oven for 45–50 minutes, until the rice is tender and the chicken reaches an internal temperature of 165°F (74°C).
When about 5 minutes remain, uncover the skillet, brush the chicken with some reserved honey-lemon sauce, and broil for 5 minutes to glaze and brown the tops.
Remove from the oven and let rest for a few minutes, then serve with lemon slices, chopped fresh parsley, and extra honey-lemon sauce on the side.