For the crust, pulse oats, flour, ½ cup brown sugar, 1 tablespoon zest, ginger, and salt in a food processor until oats are chopped. With the machine running, drizzle butter into mixture until it clumps.
Press mixture into bottom and up sides of a 9-inch square (or round) tart pan with a removable bottom. Bake crust until firm, about 20 minutes. Let crust cool to room temperature.
For the filling, combine cream cheese, sour cream, 2 tablespoons brown sugar, and remaining 1 tablespoon zest in a bowl with a mixer on medium speed until smooth. Spread mixture over crust. Line grapefruit segments on filling in rows to cover.
Sprinkle coarse sea salt over tart, slice and serve.