Heat a large pot of salted water to boil. Once water boils, add rotini and cook according to package directions.
When pasta is 4 minutes from being done, add broccoli florets to boiling water.
Once pasta is al dente and broccoli is crisp-tender, drain them together in a colander, reserving ½ cup or more of the cooking water.
Return the pasta and broccoli to the cooking pot along with a little bit of the cooking liquid. Sprinkle in the chunks of brie and swirl in the olive oil; toss just until the brie starts to melt. Season with salt and pepper. Divide between four bowls. Top each bowl with ¼ of the walnuts and serve.