Heat broth, half-and-half, salt, and pepper in a small saucepan until simmering. Add broccoli. Working in batches, purée mixture in a blender until very smooth.
Cut each sandwich into 1-in. squares.
Divide soup among 10 shot glasses. For each, push a decorative skewer* through 2 mini sandwiches and set over glass.
*We got our skewers from Pick On Us (pickonus.com).
Note: Nutritional analysis is per serving.