Preheat oven to 350°F. Grease a casserole dish. Whisk eggs with 1 teaspoon salt, 1/2 teaspoon pepper, and milk in a bowl.
Make biscuit dough: mix flour, 1/2 teaspoon salt, 1/2 teaspoon white pepper, and baking powder in a bowl. Cut butter into flour mixture to the size of peas and almonds. Stir in cream until just combined. Gather dough into a ball. Roll out from the middle in all directions until 1/2-inch thick. Using a pizza cutter, slice into 1-inch squares. Place in refrigerator to chill while making sausage.
Pulse the figs in a food processor until coarsely chopped. Brown sausage. Stir in figs with rosemary, tarragon, 1 1/2 teaspoons salt, and 1/2 teaspoon white pepper, cooking over medium low for 3 minutes.
Reserve about 1/4 cup of biscuit squares and cheese. In the casserole dish, scatter remaining biscuit squares, sausage, figs, cheese, and green onions, layering different morsels on top of one another. Pour eggs over casserole, nudging a few cheese cubes and arrange biscuit pieces around rim.
Bake for 55 minutes. Cover with foil around the 45 minute mark, once biscuits look golden and cheese is melted to continue cooking sausage egg bake until set and not jiggly. Cool for 10 minutes before cutting into it.