Boil the potatoes with skins on. Once potatoes have cooked, drain, and peel. While still hot, pass through a ricer. Transfer the potatoes to a board, quickly mix in the flour and a pinch of salt, and mix until a dough is formed. Divide the dough into small portions, and roll each one out on the floured work surface to a long rope-like form. Cut each rope into 1/2-inch lengths.
To make the sauce, heat 2 tablespoons of extra virgin olive oil in a frying pan, and add the garlic. Remove the garlic as soon as it begins to color. Add the tomato sauce, crushed tomatoes, 6 julienne cut basil leaves, and a pinch of salt. Cook for approximately 3 minutes.
Cook the gnocchi in boiling water. As soon as they rise to the surface, drain them, and add them to the tomato sauce. Add the remaining olive oil and reheat sauce with gnocchi. Add the diced cheese, salmon, and 4 julienned basil leaves. Toss for a few seconds, until the cheese is just melted.
To serve, plate on a large platter, and decorate with remaining julienne basil leaves.
Recipe courtesy of Mario Iaccorino, Don Alfonso 1890, Italy