Preheat your oven to 400°F (200°C). Pat the chicken thighs dry thoroughly with paper towels. This step is crucial for achieving crispy skin.

In a small bowl, combine the salt, pepper, paprika, and Italian seasoning. Rub the chicken thighs all over with the olive oil, then generously sprinkle the seasoning mixture over both sides, focusing heavily on the skin side. Set the seasoned chicken aside.

In a medium, oven-safe skillet or a 9x13 inch baking dish, melt the butter over medium heat on the stovetop. Add the diced shallot (or onion) and sauté for 3-4 minutes until softened and translucent.

Add the minced garlic cloves and cook for about 1 minute until fragrant. Do not let the garlic burn. Pour in the heavy cream and the chicken broth. Stir well to combine, then remove the dish from the heat.

Stir the grated Parmesan cheese into the cream mixture until smooth. Place the seasoned chicken thighs, skin-side up, into the cream sauce mixture in the baking dish. Ensure the skin remains above the liquid to crisp up.

Transfer the dish to the preheated oven. Bake for 35 to 40 minutes, or until the chicken registers an internal temperature of 175°F (80°C) near the bone, and the skin is deeply golden and crispy.

Carefully remove the baking dish from the oven. Let the chicken rest in the sauce for 5 minutes. The sauce will thicken slightly as it cools.

Garnish the dish with the freshly chopped parsley. Serve immediately, spooning the rich cream sauce liberally over the chicken and accompanying side dish.