Combine the warm water, yeast, and ¼ cup sugar in a small bowl and let it get foamy.
In a stand mixer, combine the 2 ½ cups flour and 1 teaspoon salt. Make a well in the center and pour in the yeast mixture and 2 tablespoons warm water.
Knead the dough for 5-7 minutes until smooth and elastic.
Add the 2 tablespoons of softened butter and knead until incorporated.
Place the dough in a lightly oiled bowl, cover, and let rise for 1-1.5 hours until doubled in size.
Make the cinnamon sugar filling by mixing ⅓ cup granulated sugar, 2 teaspoons cinnamon, and ½ teaspoon salt.
Make the caramel topping by melting ¼ cup butter and mixing with ⅓ cup brown sugar and a pinch of salt.
Roll the dough out into a 9x9 inch square, spread the softened butter over it, and sprinkle the cinnamon sugar filling over top.
Roll the dough into a log and cut into 9 even rounds.
Place the rounds in the pan with the caramel topping, cover, and let rise for 1-1.5 hours.
Bake at 375°F for 22-27 minutes.
Invert the buns onto a plate to serve.
