Heat oven to 350° F. Bring a large pot of salted water to boiling. Add broccoli rabe and return to a boil. Cook 1 minute, remove with a strainer and let cool. Add pasta to boiling water; cook 10 minutes. Drain.
Heat oil in a large skillet. Crumble in sausage and cook over medium-high heat until browned, 5 minutes. Meanwhile, squeeze as much water out of broccoli rabe as possible and chop. Add to sausage in skillet and cook 1 minute. Remove to a large bowl with a slotted spoon.
In a medium bowl, stir together goat cheese, Neufchâtel and egg yolks. Fold into sausage mixture.
Spread 1/3 cup marinara into bottoms of two 9 x 9-inch or 11 x 7-inch dishes. Spoon about 1 tbsp filling into each shell; place in a dish. Repeat with all shells and filling.
Divide remaining sauce between dishes. Sprinkle 1 cup mozzarella over each dish. Cover with foil and bake at 350° F for 20 minutes. Uncover; bake 20 minutes more.