In a bowl, gently mix one cup flour with mashed potatoes. Use your hands to knead the dough, adding the remaining quarter-cup flour gradually until the dough becomes soft and fluffy. Form into a ball and place in freezer for half an hour.

Once fully chilled, cut dough into four pieces. Roll each piece with your hands into a thin log, about three-quarter inches thick and 12 inches long. Cut into three-quarter-inch pieces, or to whatever size you like. They should resemble small pillows. Refreeze gnocchi until ready to cook.

Bring a large pot of generously salted water to boil. Drop gnocchi into water and boil for about three to four minutes. Use a mesh spider strainer to gently remove gnocchi. Top with sauce and shaved Parmesan, if using, and serve.

Heat oil in a large sauté pan over medium-high heat. Add onion and cook until translucent, about five minutes.

Add peppers and garlic and cook until softened, about five minutes more.

Add crushed red pepper, tomatoes and wine. Bring to a boil, then reduce heat to simmer and cook for five minutes.

Add balsamic vinegar, one-third cup water and salt and cook for five more minutes. Cool slightly. Add basil. Use an immersion blender to puree sauce until smooth.