Lightly grease a 13 x 9-inch baking pan. Set aside.
Combine all dough ingredients in the bowl of a heavy-duty stand mixer. Mix until a soft dough forms. To knead by machine, change mixing paddle to the dough hook and knead for 4-7 minutes. Knead by hand 5-8 minutes. Dough should be soft but not sticky. Place about 1 tsp oil in the bottom of a large bowl. Add dough, coat bottom of dough with oil then turn oil-side up and cover with a greased sheet of plastic wrap. Set in a warm, draft-free place to rise until double, about 1 1/2-2 hrs depending on conditions.
Bread Machine Method: Add dough ingredients per bread machine instructions. Run on DOUGH cycle and let rise in the machine.
Punch down dough. Lightly oil your work surface. Turn out dough onto prepared work surface and roll into a rectangle 12 x 16-inches.
Spread the 1/3 cup butter evenly across the top of the dough. Mix the cinnamon and brown sugar in a small bowl. Sprinkle evenly across buttered surface.
Roll up tightly starting from narrow end. Seal seam. Cut into 12 slices, 1-inch thick. Place in prepared baking pan 3 slices across short end, 4 slices down long end. Cover with greased plastic wrap and set in a warm, draft-free place to rise until double, about 45-60 minutes.
Preheat oven to 375 degrees F. Bake for 20-25 minutes or until rolls are golden brown on the top.
While rolls are baking, prepare frosting by placing cream cheese and butter in a medium bowl. Beat the butter and cream cheese well. Add the powdered sugar, 1/2 cup at a time beating until smooth. Add the orange extract and beat until well blended.
Ice rolls while still very warm.
Serve warm or cooled. Makes 12 servings (12 rolls)