Add melted butter to the bowl of a stand mixer. Warm milk to about 100°F, or until just warm to the touch. Add milk to the bowl with the melted butter.
Stir in yeast, sugar and salt. Let sit for about 5 minutes, until the yeast begins to hydrate and looks slightly foamy. Add ube extract and flour. Mix on low speed until incorporated, about 1–2 minutes.
Increase speed to medium-low and mix for about 8 minutes, or until the dough becomes smooth and begins to pull away from the sides of the bowl.
Transfer dough to a lightly floured surface and knead gently by hand for 1–2 minutes, until smooth.
Form dough into a ball and place in a lightly greased bowl. Cover and let rise until doubled in size, about 1½–2 hours.
Lightly flour your work surface and the dough. Roll into a 12 x 12-inch square. Spread softened butter evenly over the dough, leaving a 1-inch border along one edge.
In a small bowl, mix sugar, cinnamon and salt. Sprinkle evenly over the buttered dough and gently press into the butter.
Lightly moisten the exposed border with water. Starting with the edge opposite the border, tightly roll the dough into a log. Seal and cut into 9 equal pieces.
Lightly grease a 9-inch round baking dish or skillet. Place one roll in the center and arrange the remaining rolls around it.
Preheat oven to 350°F.
Bake for 25–30 minutes, until lightly browned on top or until centers reach an internal temperature of 190°F.
Let rolls cool slightly before frosting.
In a mixing bowl, whisk together powdered sugar, melted butter, vanilla extract, salt and 2 tablespoons heavy cream until smooth.
If needed, add additional cream 1 tablespoon at a time until spreadable. Spread frosting over warm cinnamon rolls and serve.
For an overnight option, prepare the dough and let it rise at room temperature for 1 hour, then refrigerate overnight. The next day, proceed with shaping. The second rise may take slightly longer.
This recipe can also be baked in an 8 x 8-inch pan with the rolls arranged in 3 rows of 3.
The simple frosting keeps the focus on the ube flavor while using accessible ingredients.