Place porcini mushrooms in a small bowl with enough warm water to cover; let stand 30 minutes.
Drain mushrooms. If a more pronounced mushroom flavor is desired, strain liquid through a fine mesh sieve and set aside. Chop mushrooms and set aside.
Using a piece of kitchen twine, tie together bay leaf, rosemary, thyme, and 2 whole cloves; set aside.
Melt 6 tablespoons butter in a large saucepan over medium-high heat. Add prosciutto and saute until golden brown, about 5 minutes. Add onions, celery, and carrots, reduce heat to medium, and cook until very soft but not brown, about 30 minutes.
In a large skillet over medium-high heat, melt 6 tablespoons butter with 1 tablespoon olive oil. Add pork and cook until golden brown, about 8 minutes. Transfer pork to vegetable mixture, reserving skillet. Add tomato paste to pork and vegetable mixture and cook 2 minutes. Meanwhile, add Marsala to reserved skillet and bring to a boil, stirring with wooden spoon or spatula, scraping up all the browned bits from bottom of pan. Pour Marsala over pork and vegetable mixture, place saucepan over medium-high heat, and bring to a boil. Immediately reduce to a simmer and cook until liquid has reduced by one-third, 30 to 45 minutes. Add chicken stock, herb bundle, and mushroom soaking liquid (if using); stir to combine. Bring to a boil, reduce heat, and let simmer, partially covered, for 2 hours. Remove from heat, season with salt and pepper; set aside to cool. Remove herb bundle.
Heat remaining tablespoon olive oil in large skillet over high heat. Add cremini mushrooms and reserved porcinis; season with salt and pepper. Cook, stirring occasionally, about 8 minutes. Fold mushrooms into pork mixture; set aside.
Preheat oven to 350 degrees, with rack in center. Melt remaining 2 tablespoons butter. Brush 12 4 1/2-by-2-inch ramekins with melted butter. Place one pasta round in bottom of each ramekin. Top round with 1 teaspoon Parmigiano-Reggiano. Using a 1 1/2 tablespoons scoop, top cheese with 1 scoop of meat mixture, then 2 teaspoons bechamel sauce. Repeat process until you have 8 layers, finishing with pasta; keep in mind you may not need to use all the pork mixture. Top final layer of pasta with bechamel sauce and sprinkle with cheese.
Transfer ramekins to baking sheet lined with parchment paper and fitted with wire rack. Cover ramekins with parchment-lined foil and bake until sauce is bubbly, about 15 minutes. Remove parchment-lined foil, increase heat to 425 degrees, and continue baking until crisp on top, about 10 minutes. Remove from oven and let stand 20 minutes. Serve immediately with extra cheese and meat sauce.