Preheat oven to 375 degrees. Line a baking sheet with parchment paper. On parchment paper, roll out the crescent dough and pinch together any holes or perforations.
In a bowl, cream together the 4 oz. cream cheese and 2 Tbsp. of granulated sugar. Spread into the center of the dough, leaving about 4" on each side. Using kitchen shears or a knife, cut diagonal 1" strips along the sides of the dough.
Rinse and cut the strawberries. In a bowl, add the remaining 2 Tbsp of sugar and the cornstarch. Mix together to coat the berries. Pour the berries over the top of the cream cheese area of the dough.
While pastry is baking, mix together the glaze by creaming together the powdered sugar, cream cheese and milk. Mix until smooth. When breakfast braid comes out of the oven, drizzle with glaze. Slice and serve.