1. Prepare the gnocchi dough: Boil the potatoes in salted water for about 30 minutes, until soft and easily pierced with a fork. Drain, peel while hot, and mash well with a potato masher in a large bowl. Add 2 egg yolks, the ricotta, flour, and all but 2 tbsp. of the Parmesan. Season to taste with salt, pepper, and nutmeg. Mix everything together, then knead about 1 minute to a silky smooth, slightly tacky dough, being careful not to over mix.
2. Lightly flour a work surface and tear off a piece of dough about the size of a tennis ball. Cover the dough in the bowl with a kitchen towel so that it doesn’t dry out as you work in batches. Using the palms of your hands, roll out the tennis ball-sized dough to form a roughly ¾-in. thick rope. With a sharp knife or pastry cutter, cut the rope into ¾-in. long pieces. Use your hands to shape the pieces into small ovals and gently depress with the tines of a fork to create the characteristic gnocchi pattern. Cover with a kitchen towel and leave the finished gnocchi on the floured work surface as you repeat with the remaining dough.
3. Have a large bowl of cold water ready by the side of the stove. Bring a pot of generously salted water to the boil. Add the gnocchi to the water and gently stir. Cook about 1 minute. The gnocchi are done when they rise to the top. Remove them with a strainer or slotted spoon and stop them from cooking by placing them directly in the bowl of cold water. Remove the gnocchi and drain well.
4. Meanwhile, heat the oven to 250°F. Halve the tomatoes lengthwise. Coarsely chop 3 cloves of garlic. Toss the tomatoes with the garlic and thyme sprigs on a baking tray large enough to accommodate the tomatoes in one layer. Drizzle with 3 tbsp. olive oil, season with salt and pepper, and toss again. Bake the tomatoes in the oven for about 1 hour 40 minutes, until they are very soft and wrinkly.
5. Prepare the dressing by finely chopping the remaining clove of garlic and placing it in a small, tall bowl with the anchovy fillets, mustard, vinegar, and remaining egg yolk. Finely blend with a hand blender while adding the sunflower oil in a thin stream. Alternatively, process in a small food processor and stream in the oil while blending. Add the remaining 2 tbsp. Parmesan and the broth. Season the dressing with salt, pepper, and lemon juice to taste.
6. In a large nonstick pan, heat the remaining 2 tbsp. olive oil and fry the gnocchi until golden brown and crispy, turning regularly as they cook. Remove the pan from the heat.
7. In a large bowl, toss the lettuce leaves with the dressing, then divide among plates or place on a large serving platter. Place the fried gnocchi and baked tomatoes over top. Serve garnished with flaked Parmesan.

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