Season chicken cutlets evenly with salt and black pepper.
Set up a standard breading station: one bowl with flour, one bowl with whisked eggs, and a third bowl containing a mixture of panko and Parmesan cheese.
Dredge each cutlet in flour, submerge in egg wash, and coat thoroughly with the panko-parmesan mixture, pressing to ensure adhesion.
Heat olive oil and 1 tablespoon of butter in a stainless steel skillet over medium-high heat until the fat shimmers.
Sauté chicken for 4 minutes per side until the internal temperature reaches 165°F (74°C) and the exterior is golden brown. Remove and rest on a wire rack.
Reduce heat to medium; add the remaining 1 tablespoon of butter and minced garlic to the skillet, cooking for 60 seconds until fragrant.
Deglaze the pan with white wine or broth, scraping the bottom to incorporate the fond.
Add heavy cream and dried oregano; simmer for 4 minutes until the volume is reduced and the sauce coats the back of a spoon.
Incorporate fresh parsley and adjust seasoning with salt and pepper.
Plate the crispy chicken and ladle the creamy garlic herb sauce over the center immediately to maintain crust texture.