Place the broccoli florets and an inch of water in a microwavable glass bowl. Cover with plastic wrap with a few holes poked in it and microwave on high for 3-4 minutes, until soft but not mushy.
Meanwhile, make two grilled cheese sandwiches. Grate the cheese, butter the outside of the bread, and make sure to cover the pan as it cooks to get an even melt and a golden brown crust. Cut each sandwich into one-inch squares.
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.
Divide the soup among 10 shot glasses. Push two mini sandwiches onto each decorative skewer and serve with a skewer balanced over each shot glass.