Cut peeled onions into approximately 1/8 inch thick slices

Melt butter or ghee in a 6-quart (or larger) stockpot.

Add onions; cook, uncovered, over low heat for 1 1/2 hours, stirring occasionally. (The long cooking time makes the onions mellow and sweet.)

Stir in pepper, paprika and bay leaf; saute over low heat 10 minutes more, stirring frequently.

Pour in broth (reserving about 8 oz) and wine. Increase heat and bring to a boil.

Dissolve arrowroot in reserved broth. Stir into boiling soup.

Reduce heat and simmer slowly for 2 hours, seasoning with salt.

Refrigerate overnight. To serve, heat soup in microwave or on stove top.

If desired, pour into ovenproof crocks or bowls.

Top with a sprinkling of grated cheese. Heat under the broiler until cheese melts and bubbles, 3-5 minutes - watch carefully!

Leftover soup can be frozen.