Step 1Heat the oven to 400 degrees. Bring a large pot of water to a rolling boil with the salt.
Step 2While the water heats, remove the tough core from the cabbage and cut into quarters vertically, then crosswise into three-quarter-inch strips.
Step 3Melt the butter in a small skillet and add the garlic and sage. Heat until the garlic just barely starts to color, then remove from the heat. Discard the garlic.
Step 4Remove the rind from the Taleggio and cut into small bits or strips. Set aside. Peel the potatoes and slice them into quarter-inch slices.
Step 5Add the cabbage and potatoes to the salted water and boil 7 to 10 minutes, until both vegetables are soft but not mushy. Using a slotted spoon, transfer to a colander set over a large bowl and let drain, then transfer to a large mixing bowl.
Step 6Bring the water back to a boil. Add the pasta to the water in the pot and cook according to package directions until al dente. Transfer to the colander to drain lightly, then immediately add to the bowl with the cabbage. Pour the melted butter over and toss until all the ingredients are well mixed. Season well with salt and pepper.
Step 7Transfer a third of the mixture to a 7-by-11-inch glass baking dish. Distribute half the Taleggio cheese over the mixture. Repeat with the remaining pasta mixture and cheese, ending with the pasta. Dust the top with the Parmigiano-Reggiano.
Step 8Bake 10 to 15 minutes, until the cheese is melted and the top noodles are slightly crispy. Let stand 5 minutes before serving.