Mix olive oil, garlic, and oregano in a small bowl and set aside.

Preheat the oven to 475 degrees F (245 degrees C).

Use a sharp thin knife to make five deep slashes at a 45-degree angle into the chicken breast, leaving about a 1/2-inch of un-cut chicken on each side.

Salt chicken breasts generously on both sides and rub the olive oil mixture into the slashes and all over the surface of the breasts.

Slide slices of chorizo into the slashes in the chicken, ensuring at least 75% of the sausage slice is covered.

Transfer chicken to an oven-safe skillet and pour in any extra oil. Dust with breadcrumbs and sprinkle with cheese.

Roast in the preheated oven until chicken is cooked through, about 20 to 25 minutes or until an instant-read thermometer reads 150 degrees F (65 degrees C).

Remove chicken from the pan and let rest on a plate covered loosely with foil.

Add vinegar and sherry to the pan, season with salt and pepper, and boil on medium-high heat, stirring occasionally, until reduced by half.

Add any accumulated juices from the chicken plate, reduce heat to low, and stir in cold butter. Stir until completely melted.