Cut the chicken breasts lengthwise in 2-3 pieces to have thinner slices. Season with salt and pepper.
Chop the onion and garlic cloves.
In a large skillet, add olive oil and butter over medium-high heat. Add the chicken and cook for 3-5 minutes per side until golden. It does not need to be completely cooked. Remove from the skillet and set aside.
If the skillet is dry after removing the chicken, add 1 more tbsp of olive oil. Fry the onion for a few minutes until soft and golden, then add the garlic and fry for another 30 seconds.
Add the flour, mix well and cook for 10-20 seconds. Then, add the wine and mix well. Let it simmer for 2 minutes until the alcohol has evaporated, and add the broth. Simmer for 1 minute, add the herbs and mix.
Add the cream, season with salt and pepper, and mix well. After a couple of minutes, put the chicken back in the pan and cook for 5 more minutes or until the chicken is cooked through.
Garnish with fresh parsley.