Heat the oven to 350 degrees. Using 1 teaspoon of butter, grease a shallow 1-quart casserole.
Melt 1 tablespoon of the butter in a small nonstick skillet. Add the onion and garlic. Cook over medium heat for 2 minutes or until tender, stirring frequently.
Place the sweet potatoes, sour cream and onion/garlic mixture in a food processor fitted with a metal blade. Process the mixture for 20 seconds or until smooth, stopping the machine and scraping down the sides if necessary. Add the parsley. Pulse 4 or 5 times or until the parsley is chopped.
Spread the potato mixture in the casserole dish.
Place the remaining 2 tablespoons of butter in a small microwavable bowl; microwave on High for 30 seconds or until melted. Add the breadcrumbs and Parmesan cheese to the melted butter; mix well. Sprinkle the mixture over the potatoes.
Bake the casserole for 25 to 30 minutes or until thoroughly heated and the breadcrumbs are golden brown.