Preheat oven to 350°F. Unroll both packages of crescent roll dough in a single layer on a floured work surface, and press together to form a 15- x 13-inch rectangle.
Stir together cream cheese, vanilla, and 2/3 cup of the powdered sugar in a medium bowl. Spread in an even layer on dough rectangle. Sprinkle evenly with graham cracker crumbs, and top evenly with chopped strawberries. Starting at 1 long side, roll up dough rectangle jelly-roll style.
Cut roll crosswise into 12 rounds, and place in a single layer in a greased 10-inch cast-iron skillet. Bake in preheated oven until browned, 25 to 30 minutes.
Stir together CannaMilk and remaining 2 cups powdered sugar in a medium bowl. Drizzle icing over warm rolls.