In a large pot of boiling, salted water, cook the broccoli until bright green, about 30 seconds. Transfer to a colander, reserving the water in the pot. Add the pasta to the pot and cook until al dente; drain, reserving 1/4 cup of the pasta cooking water.
Meanwhile, heat a 14-inch, flat-bottomed wok over high heat until a bead of water vaporizes upon contact. Swirl in 1 tablespoon oil. Add the onion and, using a metal spatula, stir-fry until it is fragrant, about 1 minute.
Swirl in the remaining 1 tablespoon oil. Add the broccoli and carrots and stir-fry until the carrots begin to wilt, about 2 minutes. Add the tomatoes, season with salt and pepper and stir-fry for 1 minute. Swirl in the cream, bring to a boil and remove from the heat. Stir in the parmesan and basil.
Add the pasta and the reserved cooking water to the wok and toss to coat; season with salt and pepper.