For the yogurt sauce: Mix the yogurt, dill, garlic, salt and oil in a bowl.
For the stuffed sweet peppers: Preheat the oven to 400 degrees F. Heat some oil in a pan. Add the onions and cook until soft. Add the carrots and cook, stirring occasionally, until soft. Transfer the onion mixture into a large mixing bowl. Fold the pork into the mixture. Add the rice, savory, dill, salt, pepper and paprika and blend well.
Fill the peppers with the pork mixture. Place the peppers on a baking pan with raised sides. Add enough water to barely cover the bottom of the pan. Cover the pan with foil and bake, about 30 minutes. Uncover the foil and bake, about 3 minutes. Serve the peppers with the yogurt sauce.