Preheat the oven to 375°F.
In a large skillet over medium-low heat, add 1 tablespoon of olive oil and the uncooked rice. Toast, stirring frequently, until the rice turns lightly golden and smells nutty, about 5–6 minutes. Remove from the pan and set aside.
Pat the chicken thighs dry with paper towels. Season both sides with 1 teaspoon of the salt, black pepper, and garlic powder.
In a large oven-safe skillet (or Dutch oven), heat the butter and remaining 1 tablespoon olive oil over medium-high heat. Add the chicken thighs and sear for 3–4 minutes per side, until deeply golden brown. (You’re building flavor here, not cooking them through.) Transfer the chicken to a plate and set aside.
Reduce the heat to medium. Add the diced shallots to the same pan, leaving the flavorful drippings behind. Cook for 2–4 minutes, until softened and lightly golden. Stir in the garlic and cook for 30 seconds, just until fragrant.
Pour in the chicken broth and heavy cream. Add the lemon zest, lemon juice, remaining ½ teaspoon salt, thyme, tarragon, and parsley. Stir well, scraping up any browned bits from the bottom of the pan.
Stir in the toasted rice and bring the mixture to a gentle simmer.
Nestle the chicken thighs back into the rice mixture. The liquid should come about three-quarters of the way up the sides of the chicken, but not fully cover it. Arrange the lemon slices over the top.
Cover with a lid (or tightly sealed foil) and bake for 25 minutes, or until most of the liquid is absorbed and the rice is tender. If needed, uncover and bake for an additional 3–5 minutes. The chicken should reach an internal temperature of 165°F.
Let rest for 5 minutes before serving. Sprinkle with grated Parmesan and fresh parsley, and serve with lemon wedges for squeezing.