First, a note on beets: they'll stain anything! Make sure you wear gloves as you're peeling the beets unless you want your hands to be an attractive magenta color!
Place the quartered beets in a large saucepan and cover with cold water. Place over medium high heat and bring to a boil. Immediately lower the heat to medium and let the beets cook for about 20 minutes or just until fork tender. Drain the beets and run them under cold water. Drain and set aside. As you're doing this, get another pot of water boiling and drop the prepped asparagus into it for just 2 minutes. Drain the asparagus and run it under cold water immediately. This is called blanching. Drain and add to the beets.
In yet another saucepan, add the water, orange blossom water, sugar and lemon juice. Bring to a boil, reduce the heat to medium and simmer until the glaze has reduced by half and has thickened slightly. Toss with the vegetables, and add the roughly chopped garlic chives. Top with the chive blossoms and crumbled goat cheese and serve as a first course on a bed of mixed greens.