Heat olive il in medium skillet until shimmering. Add chicken and sprinkle with salt and pepper. Cook 4 - 5 minutes on each side until golden brown and has reached 165°F on an instant read thermometer inserted in thickest part of chicken.
Top chicken with giardiniera, dividing equally among breasts. Sprinkle cheeses equally over vegetables. Cover pan and cook until cheeses are melted.
Garnish with parsley and serve hot.
Giardiniera packed in distilled vinegar was used and is reflected in nutrition information. Oil packed giardiniera will add significantly more calories.