In a food processor, process the ham and onions together until coarsely ground, about 10 second. Set aside.
Cut the broccoli into 3-inch florets. Slice thick stems (no need to peel) of broccoli about ½‑inch thick to yield 2 cups (use any leftover stems in another dish); place the slice stems and water in a 2-quart saucepan. Bring water to a boil and continue boiling until broccoli slices are fork tender, about 6 minutes. Remove from heat and drain well, reserving ½ cup of water. Process the cooked slices in a food processor until minced. Set aside.
Steam the broccoli florets until tender but still a bit crisp. Remove from heat and set aside.
In a 2-quart saucepan (preferably not a nonstick type) melt 1 stick of the butter over high heat. Stir in the ground ham and onions and cook until mixture starts to stick excessively to pan bottom, about 3 to 4 minutes, stirring occasionally. (The constant buildup of browned matter you will see on the pan bottom - - which is fairly easy to scrape off with a spoon - - is what gives a lot of flavor to the dish.) Reduce heat to medium and continue cooking 5 minutes, stirring occasionally and scraping pan bottom well. Add the Vegetable Magic; stir well, then continue cooking 2 to 3 minutes, stirring occasionally and scraping pan bottom well. Add the reserve ½ cup broccoli water and minced broccoli stems, stirring well; cook for 10 minutes, stirring and scraping frequently. Add the remaining 1 stick of butter and ½ cup of the bread crumbs; stir well. Cook, stirring and scraping, for about 3 minutes. If surface of mixture looks a little oily, add the remaining ¼ cup bread crumbs and stir well. Add the cream and stir, scraping pan bottom well; continue cooking and stirring about 4 minutes. Stir in the steamed broccoli, cover pan and remove from heat; let sit 10 minutes. Serve immediately.