For the Fondue
To make the fondue, bring a large saucepan filled with water to a rolling boil. Set a large bowl of ice-cold water nearby. Core each tomato, then cut a shallow X in the blossom end. A few at a time, plunge the tomatoes into the boiling water just until their skins begin to wrinkle, about 30 seconds. Then, using a slotted spoon, transfer the tomatoes to the cold water, let cool, peel, halve, and seed. When all of the tomatoes are peeled and seeded, chop them and transfer them to a bowl along with any captured juices.
In a large saucepan, warm the olive oil over medium heat. Add the onion, garlic, star anise, cinnamon, and coriander and sweat the onion until tender, about 5 minutes. Add the tomatoes and their juice, raise the heat to medium-high, and bring to a boil. Turn the heat to medium-low and simmer gently until thickened to a sauce consistency, 30 to 40 minutes. Add the vinegar and continue to cook, stirring every now and again to make sure the mixture is not sticking to the bottom of the pan, for about 1 hour longer. The fondue is ready when it is a little thicker than tomato sauce. Keep warm until serving.
For the Gnocchi
While the fondue is cooking, make the gnocchi. Preheat the oven to 350°F. Arrange the potatoes in a single layer on a sheet pan, prick each potato a couple of times with fork tines, and bake until a skewer slid into the center of a potato meets no resistance, about 45 minutes. Remove the potatoes from the oven and let them cool until they can be handled but are still warm.
Peel the potatoes and pass them through a potato ricer held over a large bowl. (You can also put the potatoes through the ricer unpeeled, but you will need to scrape the peels out of the hopper after each pass.) Let the potatoes cool until almost room temperature, then season with the salt, add the eggs, and mix thoroughly. Add half of the flour and fold it in with your hands until the flour is evenly moistened, being careful not to knead the mixture too much. Add the remaining flour and again fold in just until fully combined. Gather the dough into a rough mass.
Lightly flour a work surface and one or two sheet pans. Transfer the dough to the floured surface and knead the dough gently until smooth and soft, about 1 minute. You must not handle the dough too much or the gnocchi will be tough. Keep any dough you are not immediately working with covered with a kitchen towel to prevent it from drying out. Grasp a piece of the dough about the size of a small orange and, using your palms, roll it into a rope about 1 inch in diameter. Using a knife, cut the rope crosswise into 1-inch pieces. Pinch the center of each piece slightly, then transfer the pieces to the prepared sheet pan. Repeat until all of the dough has been rolled and cut.
Bring a large saucepan filled with salted water to a boil over high heat. Place about a dozen pieces of the cut dough into the boiling water, stir, and then wait until the gnocchi rise to the surface, which should take about 3 minutes. While the gnocchi are cooking, melt the butter in a large sauté pan over medium heat. When the gnocchi are ready, using a slotted spoon, transfer them to the sauté pan and turn them gently in the warm butter. Repeat until all of the gnocchi are cooked.
To serve, transfer the gnocchi to a warmed serving dish and spoon the warm tomato fondue over the top. Sprinkle with the Parmesan and serve immediately.
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