Preheat oven to 450ºF.
In a large bowl, stir together dry ingredients for the biscuit dough.
Cut in cold butter with a pastry blender until the mixture resembles coarse crumbs.
Make a well in the center of the flour mixture and add milk. Stir just until moistened.
Turn dough onto a lightly floured surface and knead for 5 minutes.
Roll dough out into a rectangle (approximately 1/4-inch thick).
Stir together 4 Tablespoons melted butter and 6 Tablespoons brown sugar and evenly spread filling over rectangle.
Fold rectangle in half and cut into about 1-inch strips.
Twist strips and place on a greased or lined baking sheet.
Bake in preheated oven for 10-12 minutes.
While baking, mix together 1 cup powdered sugar, 1/2 teaspoon vanilla, and a few teaspoons milk (enough to make the mixture of drizzling consistency).
Drizzle glaze over biscuit twists as soon as they come out of the oven.