In a small saucepan, bring ½ cup water and pickling spices to a boil over medium heat. Add radish; simmer for 10 minutes. Strain radish mixture, discarding any large pickling spices. Add vinegar to radish mixture, tossing to combine.
In a small bowl, stir together pickled radishes, butter, mustard, salt, and pepper.
Spread an even layer of pickled mixture onto bread slices. Place 2 corned beef slices on each of 6 bread slices. Top corned beef with remaining 6 bread slices, pickled mixture side down, to make 6 sandwiches.
Using a long serrated bread knife in a gentle sawing motion, trim and discard crusts from sandwiches. Cut each sandwich into 2 (3×1-inch) rectangles.
Serve immediately, or cover with damp paper towels, place in a covered container, and refrigerate until ready to serve.
Recipe by TeaTime Magazine at https://teatimemagazine.com/corned-beef-tea-sandwiches/