Shrimp with Lobster Sauce


1/2 lb. cooked lobster
1 tbsp minced water chestnut
1 tbsp minced bamboo shoot
1/2 tsp salt
dash of pepper
1 garlic clove
1/4 cup hot oil
1 cup chicken stock
1-1/2 lb. shrimps, shelled and deveined
1 egg slightly beaten
1 tbsp cornstarch mixed with 1/4 cup water
2 tbsp finely chopped scallions