In a large bowl, dissolve the yeast (2 1/4 tsp) in the warm water (1/2 cup, 105–115°F). Let sit about 5 minutes until foamy.
Stir in the lukewarm milk (1/2 cup), sugar (1/3 cup), softened butter (1/3 cup), salt (1 tsp), and the egg (lightly beaten). Add 2 cups of the flour and beat until smooth.
Gradually add 1 1/2 to 2 cups more all-purpose flour (use the total 3 1/2 to 4 cups as needed) until the dough is soft and easy to handle but not sticky.
Turn the dough onto a lightly floured surface and knead about 5 minutes, until smooth and elastic.
Place the dough in a lightly greased large bowl, turn to grease the top of the dough, cover, and let rise in a warm place until doubled, about 1 1/2 hours (dough is ready if an indentation remains when touched).
Punch down the dough and divide it into 4 equal portions. Working with one portion at a time, roll each quarter into a flat rectangle about as thick as a flour tortilla.
Prepare the filling: measure the 1/4 cup melted butter from the ingredient list and set aside 1 tablespoon of it for brushing after baking. In a small bowl combine the remaining 3 tablespoons melted butter, the brown sugar (1/2 cup), ground cinnamon (2 tsp), and the orange or almond extract (1 tsp). Mix until evenly combined.
Spread about one quarter of the filling mixture evenly over each rolled rectangle, leaving a small (about 1/4-inch) border along one long edge. Roll each rectangle up jelly-roll style, pinching the seam to seal.
Slice each roll into pieces of your preferred size (about 1 inch for standard rolls, about 1/2 inch for mini rolls). Arrange the slices cut-side down in a greased baking pan (leave a little space for rising).
Cover the arranged rolls and let them rise about 35–40 minutes, until roughly doubled in size. About 10 minutes before baking, preheat the oven to 375°F.
Bake at 375°F: about 10 minutes for mini rolls, or 20–30 minutes for standard-sized rolls, until golden brown and cooked through.
As soon as the rolls come out of the oven, brush the tops with the reserved 1 tablespoon melted butter to seal in softness. Let cool a few minutes, then serve.