Preheat the oven to 350 degrees F.
Cut the squash in half or thirds and place on aluminum foil in the oven. Bake until tender when stabbed with a fork, usually 30 to 35 minutes. Remove from the oven and, when it is cool enough to handle, scoop out and discard the seeds and membrane. Scoop the flesh into a strainer placed over a large bowl. Place in the refrigerator so that the squash cools and the liquid drains away. Leave for at least 6 hours or overnight.
Pass the drained squash through a ricer and then transfer to a large bowl. Add the eggs and salt. Stir well and add the flour, a little at a time, stirring to amalgamate all the ingredients. The result should be soft but not runny.
Bring a large pot of cold water to a boil. Add a pinch of salt and allow the water to return to a boil. With a teaspoon, scoop up some of the dough. Use your fingers to form the gnocchi, which should be about the size and shape of a spoon.
Cook the gnocchi in the boiling water and cook until they rise to the top of the pot. While the gnocchi cook, heat the butter over medium-high heat until it foams and subsides. Add the marjoram and radicchio, and saute over high heat for 2 minutes. Season with salt and pepper to taste. Drain the cooked gnocchi and add them to the pan with the radicchio. Toss very gently to coat. Divide the dressed gnocchi evenly among 4 warmed pasta bowls, top with the grated ricotta and serve immediately.