Greek Chicken Pasta

Name: Greek Chicken Pasta
Ingredients: 1 lb. penne; Kosher salt; 2 tbsp. extra-virgin olive oil, divided; 3/4 lb. boneless chicken breasts; Freshly ground black pepper; 1 tsp. dried oregano; 2 cloves garlic, minced; 3/4 c. half and half (or whole milk); 1 (8-ounce) block cream cheese; 1/2 c. crumbled feta cheese; 1 tbsp. lemon juice; 1 tsp. lemon zest; 1 1/2 c. halved cherry tomatoes; 1/2 c. pitted Kalamata olives, halved; 1 cucumber, chopped; 1/4 c. chopped fresh dill; Chopped fresh parsley, for serving