In a large pot of boiling salted water, cook pasta until al dente according to package instructions, about 12 minutes. Drain pasta, and return to pot; toss with 1 tablespoon oil. Cover to keep warm.
While pasta is cooking, heat remaining 5 tablespoons oil over medium-high heat in a medium saute pan. Add garlic and white parts of scallions, and cook until fragrant, about 30 seconds.
Add shrimp to pan, and cook 1 minute. Turn shrimp, and cook until pink and opaque, about 1 minute more. Stir in peas, wine, lemon zest, and red pepper; cook 1 minute.
Transfer shrimp mixture to pot; toss to combine with pasta. Drizzle lemon juice over pasta; sprinkle in green parts of scallions and the watercress. Season with salt and pepper; toss gently before serving.
When slicing scallions, remember to keep the green and white parts separate: The white pieces get sauteed with the garlic; the green are sprinkled in just before serving.