Grease your baking dish and set it aside.
In a small bowl, stir together the warm water, yeast, and sugar. Let it sit for about 5 minutes, until foamy and alive-looking.
In a medium bowl, mix the melted butter, milk, sugar, and salt. Stir in the yeast mixture.
Place the flour in a large bowl, pour in the wet ingredients, and stir until a sticky dough forms. Turn it out onto a floured surface and knead for 3–4 minutes, adding a little flour as needed, until smooth and soft. Shape into a ball.
Lightly butter a bowl, place the dough inside, cover, and let it rise in a warm spot for about 1 hour, until doubled in size.
Mix the brown sugar and cinnamon in a small bowl and set aside.
Punch down the dough and roll it into a 20×14-inch rectangle on a floured surface. Brush with melted butter and sprinkle the cinnamon sugar evenly, leaving a small border around the edges.
Roll the dough tightly from the short end into a log. Slice into 12 rolls and place them cut-side up in the baking dish. Cover and let rise again for 1 hour.
Preheat the oven to 350°F (175°C).
Bake the rolls for 25–30 minutes, until lightly golden and fluffy.
Whisk powdered sugar, milk, and vanilla until smooth. Adjust thickness as needed. Let the rolls cool for 10 minutes, then drizzle generously with glaze—or spread with cream cheese frosting if you’re feeling indulgent.