In a large pot of boiling salted water, cook pasta until al dente according to package instructions. Drain, and rinse under cold water; set aside.
Meanwhile, trim 1 inch from the stem end of broccoli stalks. Using a vegetable peeler or paring knife, peel outer layer of stalks; thinly slice crosswise. Separate florets into bite-size pieces.
Heat 1 tablespoon oil in a large skillet over medium.Add pepper flakes, broccoli, and ¾ cup water; cover and cook until broccoli is crisp-tender, 6 to 8 minutes. Uncover and cook until liquid has evaporated and broccoli is tender, 2 to 4 minutes.
In a large bowl, whisk together remaining 2 tablespoons oil, vinegar, peanut butter, and soy sauce until smooth. Add cooled pasta, broccoli, scallions, and peanuts; toss to combine. Serve immediately, or refrigerate and serve chilled.