Blend 1 cup of the thick asparagus slices and 1 cup broth until smooth. Combine the puree, remaining 2 cups broth, and 1-½ cups water in the medium saucepan and bring to a simmer. Keep warm over low heat, and do not boil.
Melt the butter in the large heavy saucepan over medium heat. Add chopped onion to pan and cook until tender, stirring occasionally, about 8 minutes. Stir in the Arborio rice and cook 1 minute, stirring constantly. Stir in the wine and cook 2 minutes or until liquid is nearly absorbed, stirring constantly. Ladle in ½ cup of the puree mixture and cook 2 minutes or until the liquid is nearly absorbed, stirring constantly. Repeat with the remaining puree mixture, ½ cup at a time, stirring constantly until each portion of broth is absorbed before adding the next (about 30 minutes total).
Stir in the remaining asparagus and cook until warm, about 2 minutes. Remove from heat and stir in ¾ cup cheese, half & half, salt, and pepper. Serve garnished with the remaining cheese.