Bring a large pot of salted water to a boil. Add the cabbage and boil until the leaves are tender, 4 to 5 minutes. Remove the pot from the heat and transfer the cabbage to a cutting board. When cool enough to handle, trim out the tough, woody core and stems and discard. Finely chop the tender leaves. You should have about 1 ½ cups chopped (150 grams).
Soak the bread in the milk in a bowl for 5 minutes. Squeeze out the bread like a sponge to remove as much milk as possible, wringing it in cheesecloth if necessary to remove and discard all the milk. Set the bread aside.
In a sauté pan over medium heat, cook the sausage and garlic clove until the sausage is cooked through. Transfer to a cutting board and finely chop it. Discard the garlic.
Combine the bread, cabbage, sausage, and flour in a bowl and stir with a wooden spoon until fully mixed. If the bread doesn’t fall apart, mash it with the spoon until it does. Taste the dough, adding salt and pepper until it tastes good to you. Stir in the eggs. Cover and refrigerate the dough for at least 2 hours or up to 24 hours.
Melt the butter in a sauté pan over medium heat. Add the bread crumbs and cook, stirring now and then, until they are toasted and golden brown, 4 to 5 minutes. Remove from the heat and set aside.
Spoon 1-inch (2.5 cm) dollops of dough into a bowl of flour. Gently scoop up a dollop with floured hands (the dough will be loose), roll the dollop into a ball, and then place it on a floured rimmed baking sheet. You should have 50 to 60 gnocchi (I yielded closer to 75).
Use the gnocchi immediately or cover them loosely and refrigerate them for a few hours. You can also freeze them in a single layer, transfer them to a zipper-lock bag, and freeze them for up to 2 weeks. Take the gnocchi straight from the freezer to the boiling water, adding 30 seconds or so to the cooking time.
Bring a large pot of salted water to a boil. Working in batches to prevent crowding, drop in the gnocchi and cover the pot to quickly return the water to a low boil. Gently cook the gnocchi until springy to the touch and tender throughout, 3 to 5 minutes. Squeeze a dumpling between your fingers. It should have some bounce-back. If it just flattens, the gnocchi are not done yet.
Using a spider strainer or slotted spoon, drain the gnocchi, letting them drip-dry for a moment, then dish them out onto warmed plates. Top each serving with a spoonful of the bread crumbs and some Parmesan.