While the chicken is in the oven, prepare your gravy.
In the same cast iron skillet in which the chicken breasts were browned, drain any residual liquid/fat (leaving the brown bits in the bottom of the pan).
Place the skillet back on the stove on medium heat. Add olive oil and butter. When butter is melted, add shallots to the pan.
Cook the shallots until they begin to soften and become translucent, about 3 minutes. Add garlic and cook for 1 more minute.
For lump-free gravy, follow this very important step: Pass flour through a fine mesh strainer, and whisk in, a little at a time. Set stove to medium high heat and continue to whisk until flour is cooked, about 1-2 minutes.
Deglaze the pan with white wine. Using a wooden spoon, scrape up all of the brown bits from the bottom of the skillet.
Add chicken broth, white wine vinegar, salt and pepper, and bring to a boil.
Once boiling, reduce to medium low heat. Add thyme and rosemary and simmer for 10 minutes.
Turn heat off and stir in heavy cream and parsley. Add salt and pepper, if needed. Spoon over chicken breasts and serve.