Reduce the heat to medium and add the remaining 1 tablespoon of oil. Add the shallot and mushrooms, and cook until golden, about 5 minutes. Add the garlic, thyme, and oregano, and cook until fragrant, about 1 minute more. Pour in the broth and scrape up any brown bits from the bottom of the pan. Slowly add in the half and half. Bring to a simmer and season with salt, pepper, and a pinch of red pepper flakes. Stir in the gnocchi and return the chicken to the pan. Let it simmer until the chicken is cooked through and the internal temperature reaches 165°F, about 8 to 10 minutes, stirring occasionally. Remove the chicken from the skillet.