Slice each chicken breast horizontally through the middle to create 4 even cutlets. Season both sides generously with salt, pepper, and garlic powder.

Heat a large skillet over medium-high heat. Add the olive oil and butter, swirling to coat the pan. Once the butter is melted and sizzling, add the chicken cutlets in a single layer. Cook for 5 to 6 minutes per side, until golden brown and cooked through (internal temperature reaches 165°F on an instant-read thermometer). Transfer the chicken to a plate and loosely cover with foil to keep warm. Turn off the heat.

Return the skillet to medium-high heat. Sprinkle in the flour and minced garlic, stirring constantly for about 1 minute until fragrant. Pour in the chicken broth and whisk vigorously to dissolve the flour. Let the liquid reduce by half, about 2 to 3 minutes.

Stir in the heavy cream and bring to a gentle bubble. Cook for 2 to 3 minutes, stirring occasionally, until the sauce thickens slightly. Remove the skillet from the heat and stir in the grated Parmesan until melted and smooth.

Return the chicken to the skillet, spooning some of the sauce over the top. Add any juices from the plate. Taste and adjust seasoning with extra salt and pepper if needed. Garnish with fresh parsley and serve immediately. For a California touch, top with sliced avocado.