1. In a bowl, with a fork, mash together feta cheese, sun-dried tomatoes, butter, 1 tsp of the oregano, 1/4 tsp of the salt, 1/4 tsp of the pepper and 2 tbsp warm water.
2. Spread 6 pieces of the chicken on a cutting board. Press about 2 tbsp of the cheese mixture down the center of each piece of chicken. Sandwich with remaining pieces of chicken, making sure to cover all the filling. Wrap each piece of stuffed chicken with 2 slices of the salami, pressing to adhere. Wrap each piece in plastic and refrigerate until cooking.
3. Place carrot sticks, green beans, 3 tsp of the oil, remaining 1/4 tsp each of the salt and pepper in a resealable plastic bag. Toss to coat; refrigerate until roasting.
4. Heat oven to 425 degrees . Heat 2 tsp of the remaining olive oil in a large stainless steel skillet over medium-high heat. Remove plastic from chicken and brown 3 pieces for 3 minutes. Flip and brown an additional 3 minutes. Transfer to a large baking dish. Repeat with remaining oil and chicken.
5. Meanwhile, spread carrots and green beans on a large baking sheet. Roast at 425 degrees for 10 minutes; stir. Add browned chicken to oven and roast veggies and chicken for an additional 15 to 20 minutes, until veggies are tender and internal temperature of chicken registers 165 degrees .
6. Warm rice in microwave 2 minutes. Stir in remaining 1 tsp oregano and the parsley. Serve with chicken and vegetables.