Add butter to small pan and place on stove top over medium high heat. After butter melts add bread crumbs and salt to taste. When breadcrumb topping begins to brown and crisp remove from heat and set aside.
Cook cavatappi according to package directions. Drain and set aside.
In large mixing bowl slowly beat together evaporated milk and eggs until evenly mixed. Add shredded cheese into mixture and mix until cheese is fully incorporated.
Add salt and pepper to taste and set bowl aside.
In large cast iron pan cook guanciale over medium heat on stove top until chucks of cured pork are crispy, about 8-10 minutes. With slotted spoon separate chunks of meat from fat. Reserve meat for later.
Add sliced shallots to rendered pork fat and sauté on medium heat until shallots begin to caramelize, about 5 minutes.
Add chopped rehydrated morels and thyme to onion and fat mixture and cook for 5-8 minutes.
After mushrooms begin to caramelize and slightly brown, deglaze pan with Madeira. Scraped bottom of pan and heat mixture until slightly thickened.
Add butter, reserved 3/4 of reserved guanciale and turn heat to medium low.
Poor cheese mixture into pan while constantly stirring. Continue mixing until cheese disappears into sauce and sauce begins to thicken. Add salt and pepper to taste.
Once sauce starts to slightly bubble, remove pot from stove and stir in noodles.
Sprinkle with bread crumb mixture and other 1/4 of reserved guanciale. Serve immediately.