In a large bowl, combine warm milk, yeast, and sugar. Let sit for 5 minutes until foamy. Add melted butter, egg, salt, and flour. Knead until smooth, then cover and let rise for 1 hour.
Lightly flour your work surface and roll the dough out into a 15x20-inch rectangle.
Spread the softened butter evenly over the dough. Sprinkle the brown sugar, cinnamon, and diced pecans evenly over the butter.
Starting at the long end, tightly roll the dough into a log. Slice the log into 12 equal segments.
Place the rolls in a greased 9x13-inch baking dish. Cover and let rise for 30 to 45 minutes.
Preheat oven to 350°F (175°C). Bake the rolls for 25 to 30 minutes until golden brown.
While the rolls bake, make the caramel sauce. In a saucepan, combine the white sugar and water. Cook over medium heat until amber in color. Carefully whisk in the butter, heavy cream, sea salt, and vanilla extract.
Pour the warm caramel sauce over the baked cinnamon rolls and sprinkle with the remaining diced pecans before serving.
Notes
Best served warm. Store any leftovers in an airtight container at room temperature for up to 2 days, or refrigerate for up to a week.