Bring 3/4 cup water to a boil in a large stockpot. Add clams; cover and cook 4 minutes or until shells open. Remove clams from pan; reserve 1 cup cooking liquid. Discard any unopened shells. Cool clams. Remove meat from shells; chop. Discard shells.
Bring 6 quarts water and 2 teaspoons salt to a boil in stockpot. Add broccoli, and cook 2 minutes or until the broccoli is bright green. Remove broccoli with a slotted spoon (do not drain water from stockpot). Place broccoli in a colander, and rinse with cold water. Drain broccoli; coarsely chop.
Return water to a boil in stockpot. Stir in pasta; partially cover, and return to a boil, stirring frequently. Cook 6 minutes or until the pasta is al dente, stirring occasionally.
While pasta cooks, heat 2 tablespoons oil in a large nonstick skillet over medium heat. Add garlic; cook 1 minute or until fragrant and beginning to turn golden, stirring constantly. Add broccoli and pepper; cook 2 minutes or until broccoli sizzles. Stir in clams and reserved 1 cup cooking liquid; bring to a boil. Reduce heat, and simmer 2 minutes or until broccoli is tender.
Add pasta to skillet, stirring well to coat. Bring mixture to a boil. Stir in remaining 1/2 teaspoon salt and chopped parsley; cook 1 minute, stirring constantly. Place about 1 cup pasta mixture in each of 6 bowls; drizzle each serving with 1/2 teaspoon oil. Serve immediately.