Put the chicken in a plastic storage bag or bowl. Add a generous pinch of salt and pepper, The Italian seasoning, and 3 tablespoons of olive oil.
Seal the bag and smush it all around to mix. Then set it aside while you start on the sauce.
Heat the butter and the remaining 1 tablespoon of olive oil in a large skillet over medium heat, then add the onion and garlic…
And cook, stirring, until they start to soften, around three minutes.
Add the roasted red peppers…
And cook until the peppers are piping hot, about three minutes.
Add the broth.
Add a pinch of salt and pepper.
Add the cream…
And bring it to a gentle boil. Reduce the heat to low, and have it simmer for five minutes, until the flavors have developed well. Turn off the heat and let the sauce cool a bit while you work on the chicken.
Heat a large skillet over medium high heat and add the chicken. Let it cook for 3 to 4 minutes on one side.
Meanwhile, transfer the sauce to a blender or food processor.
Very carefully pulse to purée.
More steps in progress