Warm the milk until lukewarm (110°F). Sprinkle the yeast over the milk with a pinch of sugar and let it sit for 5–10 minutes until frothy and fragrant.

In a large bowl, whisk together the melted butter, sugar, eggs, and vanilla. Stir in the yeast mixture until glossy.

Mix in flour and salt until a soft dough forms. Turn onto a lightly floured surface and knead for 6–8 minutes until smooth and elastic.

Place the dough in a greased bowl, cover with a warm towel, and let it rise for about 1 hour, or until doubled in size.

Punch down the dough gently and roll into a rectangle (approximately 12 by 18 inches). Spread softened butter on the dough, sprinkle with brown sugar and cinnamon.

Roll the dough tightly from the long side into a log and pinch the seam to seal. Shape into a ring, transfer to a parchment-lined baking sheet.

Cover loosely and let rise again for 30–45 minutes.

Preheat the oven to 350°F during the last 15 minutes of rising. Bake the king cake for 20–25 minutes until golden brown.

Cool on a wire rack for 10 minutes. Whisk together powdered sugar, milk, and vanilla for the glaze, and drizzle over the cake, sprinkling with sanding sugar while glaze is tacky.