Melt the butter in a saucepan and add the shallot and garlic. Cook until the shallot is wilted. Remove from heat and cool.
While the shallot and garlic cool, prepare the shrimp. If the shrimp have not been shelled and deveined, do so now. Then use a paring knife to cut a line down the back of the shrimp to the tail. Do not cut all the way through the shrimp.
Pull each shrimp apart from the cut, taking care not to completely separate the two sides. Then flip the shrimp and set it on the uncut side, and flip the tail over. Place the shrimp 2 inches apart on a baking sheet. Use a sheet of parchment paper to keep the shrimp from sticking to the pan.
Preheat the oven to 350°F.
In a mixing bowl, add the mayonnaise, lemon juice, cayenne pepper, egg, Worcestershire, mustard, salt, and pepper. Stir well to combine. Then add the cooked shallot and garlic and stir.
Add the Chex crumbs and stir well. Finally, fold in the crabmeat, being careful not to break up the crab too much.
Next, place about a tablespoon of crabmeat stuffing on the shrimp and adjust the tail so that it curls over the crabmeat. It helps to shape the crabmeat into balls so that it doesn't fall off the shrimp.
Bake for 15 minutes or until the shrimp are cooked and pink. Do not overbake.