Cook pasta to al dente, according to the instructions on the package. Drain and set aside.

Meanwhile, bring another pot of water to a boil. Cook broccoli for 2 minutes, or until bright green. Drain broccoli. Chop broccoli florets into roughly half inch pieces.

Melt butter in a large skillet, over medium high heat. Cook until butter has turned a golden color, about 4 minutes. Add chopped broccoli and sage. Sauté for 2 minutes. Add salt, pepper, and nugget and stir to combine.

Add lobster and sauté until lobster is warm. Toss the pasta with the sauce and divide among 6 plates.

Serve hot, topped with grated Parmesan cheese, if desired.