Make the green pasta dough and cut it into fettuccine. Spread the strands loosely on cloth towels.
For the sauce, cook the onion/shallot in 3 tbsp (42 g) butter until pale gold. Add the porcini and filtered soaking liquid and simmer until the liquid evaporates.
Add the ham, stir briefly, then add the cream and cook until it thickens somewhat. Turn off heat and set aside.
Roll the yellow pasta very thin.
If using a machine, join strips into one large sheet by moistening and overlapping edges about 1/8 inch (3 mm), pressing firmly, and smoothing with a rolling pin.
Lay the dough sheet flat on towels and let it dry about 10 minutes.
Cut six 8-inch (20 cm) disks, using a lid or plate as a guide.
Make the bechamel sauce to a thin, sour-cream consistency and keep it warm over very low heat.
Set a bowl of cold water near the stove. Boil 4 quarts (3.8 L) water, add 1 tbsp salt, and parboil two disks at a time no more than 30 seconds. Lift out, cool in the bowl, rinse under cold water, wring gently, and spread flat on towels.
Rewarm the mushroom and ham sauce over low heat, stirring. If using canned truffles, add the can juice to the sauce.
Bring the pasta water back to a lively boil, cook the green fettuccine, and drain when slightly underdone, firmer than al dente. Toss immediately with the sauce, add Parmesan, and toss again. If using truffle, slice it very thin over the pasta. Divide into 6 portions, keeping 6 single strands aside.
Preheat the oven to 450 F (230 C).
Butter the gratin pans. Coat a pasta disk underside with béchamel (rotate it over a pool of béchamel), spread a little béchamel on top, then set the disk in the pan with edges hanging over. Add one portion of fettuccine, keep it loose, and mix in a little béchamel. Fold the edges inward in a spiral to seal, pin with a toothpick, and wrap one reserved strand around the toothpick. Repeat for all 6.
Bake on the top rack until the folds brown lightly, about 8 minutes. Do not bake longer than 10 minutes.
Lift each bundle out with two metal spatulas onto a soup plate. Remove the toothpick without disturbing the strand. Rest at least 5 minutes before serving.