Melt butter in skillet over medium-low heat. Cook onions in butter 10 to 15 minutes, stirring occasionally, until onions are brown and caramelized. Do not hurry the process. Remove from heat.
Place all remaining ingredients in bread machine pan in the order recommended by the manufacturer.
Set to basic cycle with medium or light crust. Add onions at beep signal or 5 to 10 minute before end of kneading cycle.
Alternatively, use dough cycle. Remove dough at end of cycle, shape as desired, place on cornmeal-sprinkled baking sheet and let rise. Bake for app. 30 to 40 minutes in a 400 deg. oven. Exact time depends on shape.
Note: I generally substitute one cup of whole wheat or rye flour for one cup of the bread flour. Rye is particularly excellent.