Red-Wine Spaghetti with Broccoli

Cut broccoli into 1-inch-wide florets (with 1/2 inch of stem). Blanch in a 6- to 8-quart pot of boiling salted water , uncovered, 2 minutes. Transfer with a slotted spoon to a large colander to drain, reserving broccoli-cooking liquid in pot, then transfer broccoli to a bowl.
Return cooking liquid to a boil and cook spaghetti, stirring occasionally, 5 minutes (pasta will not be fully cooked). Drain in colander and return empty pot to stovetop. Add wine and sugar to pot and boil vigorously 2 minutes. Add spaghetti and shake pot to prevent pasta from sticking. Gently stir with tongs until coated and boil over high heat, stirring occasionally, until most of liquid is absorbed, about 6 minutes (pasta will be al dente).
Immediately after adding spaghetti to wine mixture, cook garlic and red pepper flakes in oil in a deep 12-inch heavy skillet over moderately low heat, shaking skillet occasionally, until garlic is pale golden, about 5 minutes. Add broccoli, salt, and pepper and cook, stirring, 1 minute.
Increase heat to high and pour spaghetti mixture into skillet, tossing with tongs to combine (skillet will be very full). Cook, stirring, until all of wine is absorbed, about 2 minutes. Remove from heat and stir in cheese. Serve immediately.