Cut off the bottom 1/2-inch of the endives. Cut the leaves in half lengthwise, leaving most of the smaller leaves whole. Rinse the leaves and blot them dry with a towel or place in a salad spinner to dry.
Place the endive leaves on a large plate or platter, or on individual plates. Top with the sliced radicchio, orange zest and slices, sliced almonds and shavings of Pecorino or Parmesan cheese. Top with the red wine vinaigrette (taste and add more if necessary).