Heat 1 tablespoon olive oil in a large heavy-duty skillet or pot over medium-high heat.
Season the 5–6 bone-in, skin-on chicken thighs with salt and pepper, then place them skin-side down in the hot pan. Cook 4–5 minutes until golden and browned, then flip and brown the other side for 4–5 minutes.
Stir in the minced garlic and cook about 30 seconds until fragrant, taking care not to burn it.
Add 2 cups chicken broth to the pan, cover with a lid, reduce heat to a simmer, and cook 12–15 minutes until the chicken is mostly cooked through.
Add 1 cup washed uncooked jasmine or basmati rice to the same pan, reduce heat to low, replace the lid, and simmer about 12 minutes more until the rice has absorbed the broth and is tender.
When the rice is cooked, remove the chicken thighs from the pan briefly. Gently stir in the chopped 1/2 cup sun-dried tomatoes, 1/4 cup chopped basil, and 1/2 cup shredded Parmesan until combined and creamy.
Return the chicken thighs to the pan on top of the rice, cover briefly to warm through, then serve.
Optional: For crispier skin, sear the cooked chicken skin-side down in a nonstick pan without added oil for about 3 minutes until crispy.