Put broth in a large pot and bring to a simmer. Add chicken, rice, salt, and ginger; simmer 15 minutes to let flavors develop.
Heat oil in a small saucepan over high heat until it registers 350° on a deep-fry thermometer. Fry garlic, turning constantly with a slotted spoon, until light golden brown, about 2 minutes. Transfer to paper towels to drain.
Put shallots in a small bowl and toss with flour to coat and break into rings. Fry shallots in same oil at 350° until golden brown. Drain on fresh paper towels.
Ladle soup into bowls. Top each with herbs, a sprinkle of fried garlic, a few slivers of fried shallot, and a few slices of jalapeño.
Note: Nutritional analysis is per 1 1/2-cup serving.