In mixing bowl or stand mixer with dough hook, add flour, sugar, and salt. Stir to combine.
In microwave safe bowl, combine water and milk. Heat for appox. 30 seconds, or to temp.
Add yeast and let dissolve, whisking gently to remove any lumps.
Add yeast mixture, egg, and shortening to flour mixture.
Mix at slow speed until dough forms ball and comes off sides of bowl, or by hand.
Knead dough on lightly floured surface until smooth and elastic. Place in a greased bowl.
Cover and let rise in a warm place until double in size, about 1 to 1½ hours.
Dough is ready when impression of thumb pressed in dough remains.
In the meantime, grease the inside of a 9" cast iron pan or cake pan with shortening.
When dough is raised, place on floured surface and punch down with the heel of your hands.
Keeping surface floured, roll into a large rectangle approx. 9" x 15"
Spread butter over entire surface of dough.
In a medium bowl, add berries. Sprinkle with extract, then add sugar. Gently toss to mix.
Spoon fruit into the center lengthwise, approx. 5" in width.
Gently fold each long side of dough over fruit to the center, close to edges but do not overlap.
Using a knife, cut center lengthwise. Turn both sides from opposite ends to form twist.
Place the twist in a circle in prepared pan.
Bake for approx. 25-30 minutes or more until golden on top and fruit is bubbling.
Make sure dough is cooked though. Use toothpick inserted into center to test for doneness.
Remove from oven and set aside.
Meanwhile, in a small bowl whisk together the sugar, milk, and vanilla until smooth.
Drizzle over fruit danish while still warm.
Allow to cool to room temperature.
Slice and serve.