Heat your oven to 400 degrees F and place a large oven-safe sauté pan or cast-iron skillet over medium-high heat.
Set out your chicken on a clean work surface and pat it dry with paper towel. Season well with salt and pepper. Scatter the flour into a shallow dish and add the chicken, tossing to coat with flour.
When the pan is hot, add 1 tablespoon of the oil and place the chicken in the pan, skin side down. Sear until golden brown, about 8 minutes. Flip the chicken over, transfer to a sheet pan and place in the oven to continue cooking until cooked through and the internal temperature reaches 165 degrees F, 8 to 10 minutes. Remove the chicken from the oven and allow it to rest while you make the pan sauce.
Turn the heat under the pan to medium and add the remaining tablespoon of olive oil. Add the shallot, season with salt and pepper and cook just until translucent, 2 to 3 minutes. Add the garlic, cook for another minute, then carefully pour in the broth and cream.
Allow the sauce to simmer until slightly thickened, about 5 minutes, then whisk in the Dijon mustard, then the Parmigiano-Reggiano and lemon zest and juice. Season to taste with salt and pepper and add the chicken and olives to the sauce. Simmer for another few minutes then scatter over the parsley and oregano just before serving.
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