Trim tough ends from broccoli stalks. Cut broccoli heads crosswise into 3 inch lengths. Cut stalks lenghtwise into 1/3 inch thick lices. Cut flowerets in half if they are thicker than 1 1/2 inches, leave smaller flowerets whole.
In a large 6 quart pan cook broccoli, uncovered, in about 3 quarts boiling water just until barely tender when pierced (about 5 to 6 minutes). Drain well and arrange in shallow 4 quart casserole. Keep warm.
While broccoli cooks blend cornstarch into 1 1/3 cups cold water, set aside.
Wipe pan dry and add onions and oil Cook over high heat, shaking pan often, until onions are browned (about 6 to 8 minutes).
Remove onions and set aside. Keep warm.
In pan bring sherry, broth, vinegar, sugar, and currants to boil. Boil uncovered until mixture is reduced to 1 1/3 cups (about 6 to 8 minutes). Stir in cornstarch mixture; bring to boil, stirring. Season to taste with salt.