Stir 1/2 cup plus 2 1/2 tablespoons lukewarm milk, yeast, and sugar together in a bowl. Let stand until foamy, about 5 minutes.
Mix tipo 00 and bread flours together in a bowl. Make a well in the center. Add beaten eggs and yeast mixture. Mix together with a fork. Add water and mix again to form a sticky ball. Knead butter into the dough a little bit at a time.
Transfer dough to a floured work surface and knead vigorously until smooth, about 10 minutes. Place in a lightly floured bowl, cover with a clean, damp cloth and let rest in a warm place until doubled in volume, about 1 1/2 hours.
Turn dough out on a floured surface. Stretch out one piece and fold it over the top. Repeat with another section of dough, working your way around the circle. Place dough in a paper panettone mold. Cover with plastic wrap and let rise in a warm place until dough reaches the rim of the mold, about 2 hours.
Preheat oven to 350 degrees F (175 degrees C). Fill a baking dish with some water and place it on the bottom rack of the oven to keep the panettone moist as it bakes.
Brush the top of the panettone with some milk and place the mold on a flat baking sheet.
Bake in the preheated oven until a skewer inserted into the middle comes out clean, 40 to 45 minutes. Allow to cool on a wire rack for a few minutes. Pierce the side, near the bottom, with 2 long wooden skewers that will stick out the other side. Flip the panettone gently and set the skewers on the rim of a tall pot. Cool panettone upside down so it doesn’t collapse, at least 5 hours.
Mix tuna and mayonnaise together in a bowl until smooth. Blend olives, olive oil, anchovy fillets, and capers in another bowl until smooth. Mix cream cheese and ham together in a third bowl.
Remove skewers gently from the panettone and slice lengthwise to obtain 6 slices, including the top. Lay the bottom slice on a serving plate; spread with tuna mixture. Cover with shrimp and lettuce. Press second slice on top; add third slice. Spread olive mixture on top and cover with mozzarella cheese. Press fourth slice on top; add fifth slice. Spread cream cheese mixture on top and cover with prosciutto. Cover with the top slice.
Wrap panettone in plastic wrap and refrigerate for at least 1 hour before serving. Slice into wedges from top to bottom.