In bowl, whisk together eggs, basil, ½ tsp (5 mL) salt and pepper. Set aside. Place potatoes in large saucepan and cover with cold salted water; bring to a boil. Cook 12 to 15 min. until tender. Drain well.
While still hot, pass potatoes through a ricer onto lightly floured work surface. Mound riced potatoes and a make a well in the centre. Allow potatoes to cool until barely warm. Pour egg mixture and 1¼ cups (300 mL) flour into the well. Using a fork, stir flour and egg mixture to gradually incorporate potatoes to form dough. Gently knead dough, adding remaining flour a bit at a time, as needed, just until a smooth dough comes together.
Divide dough into 6 portions. Roll each portion into 1/2-in. (1-cm) thick rope. Cut ropes into 1-in. (2.5-cm) pieces. Lightly roll each piece on tines of fork to create indentations. Line a baking sheet with clean tea towel lightly dusted with flour. Arrange gnocchi in single layer on tea towel. Freeze 2 hr. or until frozen through. Transfer gnocchi to airtight container or re-sealable freezer bags. Freeze up to 1 month. Or gnocchi can be cooked immediately after rolling.
To cook: Add batches of fresh or frozen gnocchi into large saucepan of boiling salted water. Cook 3 to 5 min., until gnocchi float to surface. Remove with slotted spoon. Toss gently in warm tomato sauce or melted butter. Serve sprinkled with Parmesan cheese.
A ricer ensures potatoes will be very smooth which is essential for light-textured gnocchi.