To a large pot of salted, boiling water add spaghetti and cook until al dente. Reserve 1/3 cup cooking liquid and drain pasta in a colander. Return pasta to kettle with reserved liquid.
While pasta is cooking, in a large heavy skillet heat oil over moderate heat until hot but not smoking and cook broccoli with salt, to taste, stirring occasionally, until crisp-tender, about 5 minutes. Add garlic and cook, stirring, until golden, about 30 seconds.
To pasta add broccoli mixture, Brie, and walnuts, tossing until cheese is just melted, and season with salt and pepper.
Recipe courtesy of Gourmet Magazine