In the bowl of a food processor, pulse half of the shrimp with the chicken, egg, fish sauce, oyster sauce, sesame oil, sambal oelek, and garlic until smooth and sticky. Add the remaining shrimp, green onion, and cilantro. Pulse for a few seconds, just until the shrimp are chopped and still have a bit of a coarse texture. Transfer into a bowl. To keep the mixture cold, place the bowl of shrimp over a bowl filled with ice.