Combine warm milk, sugar, and yeast; let sit 5–10 minutes until foamy.
Mix flour, salt, yeast mixture, egg, and butter into a sticky dough.
Knead 5–7 minutes until smooth; place in oiled bowl and cover.
Let dough rise 1 hour until doubled.
Punch down and roll into 12×8-inch rectangle.
Brush with butter and sprinkle brown sugar, cinnamon, and nuts.
Stack strips, slice center leaving one edge, then twist for branches.
Shape into tree on parchment-lined sheet; pinch base for trunk.
Let rest 30 minutes for second rise.
Bake at 350°F for 20–25 minutes until golden.
Mix powdered sugar, milk, and vanilla to make glaze.
Cool 10 minutes, then drizzle glaze over bread.