Combine garlic, chili, ginger and 1/3 of the shrimp in a food processor and purée, stopping machine to scrape down sides of container as necessary. Add remaining shrimp along with shallots, bell pepper, salt, pepper and cilantro, and pulse as many times as necessary to chop shrimp, but not too finely. Shape mixture into 4 patties. Chill for 15 to 20 minutes.