Preheat oven to 350°F Spray a 9 x 13 baking dish with nonstick spray.
Bring a large pot of water to a boil. Add the pasta and cook 5 minutes. Add the broccoli and cook, stirring occasionally, until the pasta and broccoli are tender, 3-4 minutes. Drain; return the broccoli and pasta to the pot.
While the pasta and broccoli are cooking, heat the oil in a large saucepan over medium heat. Add the onion and cook, stirring occasionally, until tender, about 5 minutes. Add the flour and mustard; cook, stirring constantly, about 1 minute. Gradually whisk in the milk and salt. Increase the heat and cook, whisking constantly, until the sauce boils and thickens, 3-4 minutes.
Add the sauce to the pasta and broccoli. Stir to combine. Transfer to the prepared baking dish and sprinkle evenly with the cheese. Bake until bubbling,about 25 minutes.