Combine all but butter in medium saucepan and bring to boil. Boil down to 1 cup, about 20 minutes. Set aside. Can be made ahead.
Combine all in plastic bag and marinate shrimp for at least 30 minutes and up to an hour.
Sauté mushrooms in pan with olive oil and unsalted butter until slightly golden, add salt and pepper. Set aside.
Cook pasta in a large pot of boiling salted water, then drain.
Reheat sauce base on low and whisk butter in 2 tablespoon increments until incorporated in sauce. Don’t overheat! Keep warm.
Heat broiler. Drain shrimp and place on broiler pan keeping the shallots from the marinade. Broil until opaque and tails slightly singed.
Add mushrooms to pasta and toss to combine.
Mound pasta in middle of each bowl and place 4 shrimps on top of pasta.
Spoon sauce around base of pasta and sprinkle fresh herbs and grated Parmesan on top.