Place flour, thyme, parsley, and ¼ teaspoon salt in food processor. Add butter. Cover and pulse until mixture resembles coarse crumbs. Sprinkle 1/4 cup ice water over flour mixture. Cover and pulse. Continue sprinkling enough of the remaining ½ cup ice water, 1 tablespoon at a time, and pulsing until the flour mixture is moistened and holds together. Shape mixture into a ball. Wrap pastry dough in plastic wrap and refrigerate 10 minutes.

Preheat oven to 400°. Line a large rimmed baking pan with parchment paper. Brown sausage in a medium nonstick skillet over medium heat. Transfer to medium bowl to cool; set aside.

Whisk together 4 whole eggs, milk, remaining ¼ teaspoon salt and pepper in a medium bowl. Heat same skillet over medium heat. Pour egg mixture into skillet. When bottom begins to set, use a spatula and stir the mixture to form large curds. Continue cooking and stirring until eggs are cooked through but still glossy. Add to sausage in bowl.

Heat oil in same skillet over medium-high heat. Add hash browns; cook until crispy and golden brown, stirring frequently. Add to egg mixture in bowl; stir in shredded cheese until combined and set aside.

Roll chilled pastry dough on a lightly floured surface into a 16x12-inch rectangle. Cut dough into 12 (4-inch) squares. Mound scrambled egg mixture in center of 6 squares.

Beat egg white with fork in small bowl; brush on edges of square with filling. Top with remaining squares. Press edges together; crimp edges with the times of a fork to seal. Place filled pastries in prepared baking pan; brush tops with remaining egg white. Cut 2 small slits in tops of each filled pastry to vent steam. Lightly sprinkle with sea salt. Bake 28 to 32 minutes or until golden brown.