01 - Combine warm milk and yeast in a large bowl. Let stand for 5 minutes until mixture becomes foamy, indicating the yeast is active.
02 - Add sugar, melted butter, egg, and salt to the yeast mixture. Whisk until well combined. Gradually incorporate flour, mixing until a soft, tacky dough forms.
03 - Turn dough onto a lightly floured surface. Knead for 5 to 7 minutes, folding and pressing until dough becomes smooth, elastic, and no longer sticky.
04 - Place dough in a greased bowl, turning once to coat. Cover with plastic wrap or a clean towel. Let rise in a warm, draft-free area for 1 hour or until doubled in size.
05 - While dough rises, combine brown sugar and cinnamon in a small bowl. Mix until evenly blended.
06 - Punch down risen dough and roll into a 12x16-inch rectangle. Spread softened butter evenly over surface. Sprinkle cinnamon-sugar mixture across the dough, leaving a small border around edges.
07 - Fold dough in half lengthwise to encase filling. Cut crosswise into 12 equal strips. Twist each strip 4 to 5 times and place on a parchment-lined baking sheet, spacing 2 inches apart.
08 - Cover twists loosely with plastic wrap. Let rise for 15 minutes while preheating oven to 375°F.
09 - Bake for 18 to 20 minutes until twists are deep golden brown and cooked through. Rotate baking sheet halfway through for even browning.
10 - While twists bake, whisk powdered sugar, milk, and vanilla extract in a small bowl until smooth and ribbon-like. Adjust consistency with additional milk if needed.
11 - Drizzle warm glaze over slightly cooled twists. Serve immediately while still warm for best texture and flavor.