In a small bowl, combine the warm milk, yeast, and ½ teaspoon granulated sugar. Allow the mixture to stand for approximately 5 minutes, or until foamy.

In the bowl of a stand mixer fitted with a dough hook, combine the flour, salt, and granulated sugar. Add the yeast mixture and mix until a soft dough begins to form.

Add the softened butter, one tablespoon at a time, mixing well after each addition. Knead the dough on low speed for approximately 5 minutes, until smooth and elastic.

Shape the dough into a ball and place it back into the bowl. Cover and allow it to rest in a warm area for about 30 minutes, or until doubled in size.

Transfer the dough to a lightly floured surface and roll it into a 10 x 20–inch rectangle.

Brush the melted butter evenly over the dough. Sprinkle the brown sugar, granulated sugar, and cinnamon evenly over the surface.

Starting from the long edge, roll the dough tightly into a log. Slice into 8 equal portions.

In a small saucepan over low heat, combine the butter, brown sugar, vanilla extract, cinnamon, heavy cream, and salt. Bring to a gentle boil, then reduce heat and whisk until the sugar dissolves and the mixture is smooth.

Grease a 9 x 12–inch baking dish. Pour the caramel mixture evenly into the pan and sprinkle with chopped pecans.

Arrange the sliced buns on top of the caramel mixture. Cover and allow them to rise in a warm location for approximately 30 minutes.

Preheat the oven to 350°F (175°C).

Bake for 25–30 minutes, or until the buns are fully baked and the centers are no longer doughy.

Remove from the oven and allow the buns to rest for 15 minutes. Carefully invert onto a parchment-lined tray before serving.