Melt butter in a saucepan over medium heat. Cook onion and garlic in butter until soft and golden brown (do not allow the garlic to burn). Remove from heat.
Combine cream cheese, Swiss cheese, oregano, basil and black pepper in a medium bowl. Stir in onion mixture.
Lay out one sheet of phyllo dough on a flat surface (cover the phyllo dough that you are not using with a damp kitchen towel to keep it from drying out). Brush with oil and fold in half lengthwise.
Place one heaping tablespoon of filling onto one end of the pastry, leaving ¾ inch on each side of filling. Roll up the pastry to enclose the filling and twist each end.
Freeze the twists in plastic freezer container for up to 2 months.
When ready to serve, preheat oven to 375 degrees. Bake the twists frozen on a cookie sheet for 20-30 minutes until golden brown.