In a small bowl, dissolve yeast in warm water. Let stand until creamy, about 10 minutes.
In a large bowl, combine yeast mixture with sugar, salt, egg and 1 cup flour, stirring to combine. Stir in remaining flour, ½ cup at a time, beating well with each addition. When dough has come together, remove onto a lightly floured surface and knead until smooth and elastic, about 8 minutes. Cover with a damp cloth and let rest for 10 minutes.
Lightly grease an 8-inch square baking pan. Roll dough out on a lightly floured surface to ¼-inch thick rectangle. Smear dough with butter and sprinkle with cinnamon and brown sugar.
Roll up dough along the long edge until it forms a roll. Slice roll into 16 pieces and place in pan with the cut side up.
Cover pan and let rise at room temperature until doubled in volume, about 45 minutes.