Soak shitake mushrooms in hot water for 30 minutes. Use wet paper towel to keep mushrooms submerged in water.
Cut chicken thighs into thin slices; then cut again into matchstick strips. Mix with Chicken Marinade ingredients. Cover and refrigerate.
Coarsely chop shrimp. Cover and refrigerate.
Heat wok until very hot. Swirl in 1 1/2 tablespoons oil, then add chicken pieces in single layer. Flip chicken over when underside is brown, about one minute. Break up pieces with spatula. Use slotted spoon to transfer chicken to a plate.
Add shrimp and stir-fry until just cooked through, about 30 seconds. Transfer to a plate.
Heat wok until very hot. Swirl in 1 1/2 tablespoons oil, then add mushrooms, celery, cabbage and bamboo shoots. Stir-fry until cabbage softens, about 3 minutes. Add salt and toss. Return chicken and shrimp to wok and toss with vegetables. Stir cornstarch slurry and swirl into wok along perimeter of wok. Toss well until mixture thickens. Transfer to plate, cover and refrigerate to chill.
Whisk egg in a small bowl with a fork until frothy. Have damp cloth or paper towel handy to cover wrappers so they don't dry out.
Place one spring roll wrapper on flat surface. Spoon 2 tablespoons of filling onto lower corner of wrapper, spreading into a 4" line.
Fold bottom edge over filling and roll wrapper to the center.
Bring two end flaps towards center of wrapper and gently press down.
Brush exposed edges of wrapper with beaten egg. Finish rolling spring roll towards top corner into cylinder shape.
Repeat with remaining wrappers and filling. Place finished spring rolls on plastic wrap lined platter. Cover with plastic wrap until ready to fry.
Pour enough oil into a skillet to reach halfway up spring rolls during frying process. Heat oil to 350 degrees or use bamboo chopstick to test for readiness. When oil is hot enough, small bubbles will form around the chopstick when inserted into the oil.
Place a few rolls into hot oil and fry on both sides until crisp and golden brown. Do not overcrowd. Drain on paper towels. Keep warm in 200 degree oven. If you want to fry spring rolls ahead of time, reheat in 400 degree oven for 8-10 minutes.
Adapted from Florence Lin's Complete Book of Chinese Noodles, Dumplings and Breads