Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
Melt 1 1/2 tablespoons butter in a medium saucepan over medium heat. Stir in flour and cook for 2 minutes. Slowly stir in milk and cream; simmer, stirring constantly until thickened. Stir in pesto, parsley, garlic, Parmesan cheese, 1 teaspoon salt, white pepper, Worcestershire sauce and Tabasco sauce. Reduce heat to low and allow to simmer.
Meanwhile, place broccoli in a steamer over 3cm boiling water and cover. Cook until tender but still firm, about 2 to 6 minutes. Drain.
Melt 1 tablespoon butter in a large frypan. Saute prawns, garlic and 1 teaspoon salt for 5 minutes or until prawns are pink.
In a large bowl, toss pasta, prawns and broccoli; pour sauce over and serve.