Heat the olive oil in a large, deep pot or dutch oven over medium-high heat.
Season the chicken breast cubes with basil and oregano and cook until lightly browned on all sides, about 5 minutes, turning occasionally.
Add the garlic, shallots, capers, olives, and spinach, and continue to cook for 1 minute. Deglaze the pan with wine vinegar.
Mix in the dry pasta. Add in the white wine and chicken stock, making sure there is enough to just cover the pasta (if not, add a bit more chicken stock).
Season with red pepper flakes and pepper to taste.
Bring to a low boil until pasta is almost al dente, about 15-20 minutes, stirring often.
Reduce to low heat and add in the heavy cream, feta and cherry tomatoes, red pepper and mushrooms.
Mix well and continue to simmer for 5-10 minutes, checking the pasta to get to you desired consistency.