Combine the softened cream cheese, shredded cheddar, ranch dressing, and chopped green onion in a bowl. Mix until smooth and fully blended. Set aside.

Pat the chicken breasts dry with paper towels. Rub all over with 2 tablespoons of olive oil and season both sides with kosher salt and black pepper.

Using a sharp paring knife, cut a wide pocket into the thick side of each chicken breast. Angle the blade toward the center and cut as deep as possible without breaking through the other side.

Divide the cream cheese filling evenly between the four pockets. Press the opening gently closed and secure with toothpicks if needed.

Heat the remaining 2 tablespoons of olive oil in a large skillet over medium-high heat until shimmering. Sear the stuffed chicken breasts for 3 to 4 minutes per side until deeply golden brown but not fully cooked through. Work in batches if needed.

Return all four chicken breasts to the skillet. Pour the Buffalo sauce evenly over them. Cover with a lid, reduce heat to low, and cook for about 15 minutes until the internal temperature reaches 165 degrees F.

Remove the lid and spoon the pan sauce back over the chicken. Remove any toothpicks. Serve drizzled with extra ranch and Buffalo sauce, topped with crumbled blue cheese and fresh green onions.