Cook potatoes. (Bake at 400° for 1 hour or until very soft. Or microwave for 7-10 minutes or until very soft.)
While potatoes are warm, cut in half and scoop insides out into a bowl. Discard potato skins. Mash potatoes in bowl. Using a hand mixer, finely mash potatoes. Add potato starch and egg yolks; combine with hand mixer to make a dough.
Divide dough into six parts. Working with one part at a time, roll out onto a surface lightly sprinkled with potato starch. Roll dough into a long rope, about 3/4-inch thick. Cut rope into 3/4-inch pieces. Roll each piece down the tines on the back side of a fork to create ridges. Place each piece onto a tray lined with parchment paper. If using soon, chill until ready for use. Or freeze for up to a month.
When ready to cook, heat lightly salted water about 2-inches deep in a deep skillet. When the water is gently simmering, add gnocchi and cook for 2 minutes. Remove gnocchi with a slotted spoon to a plate until sauce is ready.
To make Sauce:
Heat olive oil and butter in a large skillet. Add cherry tomatoes and cook for 5 minutes, covered, or until tomatoes begin to pop, stirring occasionally. Stir in garlic; cook an additional 1-2 minutes. Remove from heat and stir in basil.
Combine gnocchi, sauce, and mozzarella balls in a large bowl. Divide evenly among 6 bowls; top evenly with Parmesan cheese.
Per serving (about 1 1/2 cups), Calories 411, Fat 17g, Cholesterol 81mg, Sodium 303mg, Carbohydrates 51g, Fiber 6g, Potassium 33% DV, Protein 15g, Vitamin C 48% DV