Place chicken cutlets between parchment paper and pound to a uniform 0.5-inch thickness.
Prepare a breading station with three shallow bowls: flour in the first, beaten eggs in the second, and a mixture of Panko, 0.5 cup Parmesan, and oregano in the third.
Dredge each cutlet in flour, dip in egg wash, and press firmly into the Parmesan-breadcrumb mixture to ensure full coverage.
Heat olive oil in a large skillet over medium-high heat. Sear chicken for 4 to 5 minutes per side until the crust is golden brown and the internal temperature reaches 165°F (74°C). Remove chicken and tent with foil.
Reduce heat to medium. In the same skillet, melt the butter and sauté minced garlic for 60 seconds until fragrant.
Whisk in the heavy cream, scraping the bottom of the pan to deglaze. Bring to a gentle simmer for 3 minutes until slightly reduced.
Whisk in 0.25 cup Parmesan cheese until the sauce is smooth and emulsified. Season with salt and pepper.
Plate the chicken, drizzle with the garlic cream sauce, and garnish with fresh parsley.