Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Season chicken thighs with salt, pepper, and paprika on both sides.
Place chicken thighs skin side down in the skillet and sear for 5-6 minutes until the skin is golden brown and crispy. Flip and cook for an additional 3 minutes. Remove chicken from the skillet and set aside.
Reduce heat to medium and add diced onion to the skillet. Cook for 3-4 minutes until softened.
Add minced garlic and cook for 30 seconds until fragrant.
Add rinsed rice to the skillet and stir to coat the rice with the oil and onion mixture.
Pour in chicken broth and whole milk, then stir in dried thyme.
Return the chicken thighs to the skillet, placing them on top of the rice mixture.
Bring the liquid to a gentle boil, then reduce heat to low and cover the skillet with a tight-fitting lid.
Simmer for 25 minutes without lifting the lid, until the rice is tender and the chicken is cooked through (internal temperature 165°F/74°C).
Remove the lid and stir in frozen peas and grated Parmesan cheese. Cover and cook for an additional 2-3 minutes until peas are heated through and cheese is melted.
Adjust seasoning with additional salt and pepper if needed.
Serve hot, spooning creamy rice and chicken onto plates.