Place ginger, cilantro, garlic, broth, and lemongrass in a large saucepan, and bring to a boil. Cover, reduce heat, and simmer 20 minutes. Strain the mixture through a sieve over a bowl; discard solids. Return infused broth to pan. Add coconut milk, fish sauce, sambal oelek, chicken, and mushrooms; bring to a boil. Reduce heat, and simmer 10 minutes. Add peas; cook 3 minutes. Remove from heat; stir in basil and lime juice.