Heat oven to 375 degrees. Pulse granola and sugar in a food processor until finely chopped. Drizzle butter over granola mixture and pulse to combine. Press mixture into and up sides of a 9-inch pie dish. Bake until golden, about 10 minutes. Transfer to a wire rack and let cool.
Beat cheese in a mixer until smooth. Add yogurt, honey, and ginger; beat until combined.
Pour filling into prepared crust and chill in refrigerator until set, at least 6 hours and up to 1 day. Just before serving, arrange mango on top of pie and drizzle with honey.