In a small bowl, combine warm milk and yeast. Let sit until foamy, about 5 minutes.

In the bowl of a stand mixer, combine flour, sugar, and salt. Add eggs, vanilla, and yeast mixture. Mix until dough forms.

Add butter, one tablespoon at a time, until incorporated. Knead until smooth and elastic, about 10 minutes.

Place dough in a greased bowl, cover with plastic wrap, and let rise until doubled in size, about 1.5 hours.

Roll the dough out into a rectangle. Spread butter over the surface, and sprinkle with brown sugar and cinnamon.

Roll the dough up tightly from the long side, pinch the seam to seal it, and cut in half lengthwise.

Twist the two pieces together, keeping the cut sides facing up, and place in a loaf pan.

Cover with a cloth and let rise for another 30 minutes. Preheat the oven to 350°F (175°C).

Bake until golden brown, about 40 to 45 minutes. Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.