Step #1 Place the potatoes In a large-ish pot & just cover with cold water.
Step #2 Boil the whole potatoes until they are soft, about 45 mins.
Step #3 While still warm, peel the potatoes & pass them through a food mill onto a clean pasta board.
Step #4 Make a well in the center of the potatoes & sprinkle with the flour.
Step #5 Place the egg & salt in the center of the well and, using a fork, stir the egg into the flour & potatoes.
Step #6 Bring the dough together, & continue to knead for another 4 mins, kneading carefully until a ball is formed, until the dough is dry to the touch.
Step #7 Cut a tennis-ball sized hunk of dough off the main ball & roll it into a dowel about 3/4-inch thick.
Step #8 Cut across the dowel to form pellets about 1 inch long.
Step #9 Flick each pellet down the tines of a fork to form the traditional gnocchi shape.
Step #10 Repeat with the remaining dough.
Step #11 In a 14 to 16-inch frying pan, tomato sauce, mix the pepper flakes, & 1 tsp salt.
Step #12 Bring to a boil, & let simmer 15 mins, reduce the heat, or until the sauce is as thick as good porridge.
Step #13 (At this point the sauce could be put in the fridged for up to 2 days).
Step #14 When you are ready to serve the gnocchi, bring 6 quarts of water to a boil & add 2 tbsps salt.
Step #15 Drop the gnocchi into the boiling water & cook this until floating aggressively, 4 to 5 mins.
Step #16 Carefully transfer the gnocchi to the pan with the sauce, using a slotted spoon.
Step #17 Turn the heat to medium & toss carefully for about 30 seconds.
Step #18 Tear the basil leaves into a few pieces & add to the sauce along with the mozzarella cubes.
Step #19 Toss together for 30 seconds longer.
Step #20 Pour into a heated bowl & serve as soon as possible.
Step #21 BASIC TOMATO SAUCE: In a 3-quart saucepan, heat the olive oil over med-heat/flame.
Step #22 Add the onion & garlic & cook this until soft & light golden brown, about 8 to 10 mins.
Step #23 Add the thyme & carrot & cook 5 mins more, until the carrot is quite soft.
Step #24 Add the tomatoes & juice & bring to a boil, stirring often.
Step #25 Lower the heat & let simmer for 30 mins until as thick as hot cereal.
Step #26 Spice up with salt & serve.
Step #27 This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.