Prepare Chicken: Pat the chicken breasts or thighs dry with paper towels. Season generously with salt and black pepper on both sides. If using larger chicken breasts, you can slice them horizontally to create thinner cutlets for quicker, more even cooking.
Sear Chicken: Heat the olive oil in a large skillet or non-stick pan over medium-high heat. Add the seasoned chicken and sear for 5-7 minutes per side, or until golden brown and cooked through. Internal temperature should reach 165°F (74°C). Remove the chicken from the skillet and set aside on a plate, tented with foil to keep warm.
Sauté Garlic and Deglaze: Reduce the heat to medium. Add the minced garlic to the same skillet and sauté for about 30 seconds until fragrant, being careful not to burn it. Pour in the dry white wine and scrape up any browned bits from the bottom of the pan with a wooden spoon. Let the wine simmer for 2-3 minutes, reducing slightly.
Simmer Sauce: Stir in the chicken broth and bring to a gentle simmer. Slowly pour in the heavy cream, stirring constantly. Continue to simmer the sauce gently for 5-7 minutes, or until it begins to thicken. Do not bring the sauce to a rolling boil, as this can cause the cream to curdle.
Add Gorgonzola: Remove the skillet from the heat. Add the crumbled gorgonzola cheese to the warm cream sauce, stirring until it has completely melted and incorporated, creating a smooth and luscious sauce. Taste the sauce and adjust seasoning with salt and pepper as needed. Gorgonzola can be salty, so season carefully.
Combine and Serve: Return the cooked chicken to the skillet, spooning the creamy gorgonzola sauce over each piece. Garnish generously with fresh chopped parsley. Serve immediately with your favorite side dishes.