"Country Style" Onion Soup - cooking recipe

Ingredients

3 2 1/2 medium white onions (sweet onions are especially good) or 2 1/2 medium yellow onions (sweet onions are especially good)
1/2 cup unsalted butter
1/4 - 1/3 cup flour (two small fistfuls)
2 2 cups homemade chicken stock or 2 cups canned low sodium chicken broth
water
salt

Preparation

Slice onions in half latitudinally, peel, cut off tops. Cut in half again, the other way. Turn on the flat side and cut each quarter into thirds or fourths, to get fairly uniform, fairly thin half-rings of onion.
In a sturdy saucepan over medium-high heat, melt butter. Watch carefully to make sure it doesn't separate.
Just before butter melts completely, add onions. Cook, stirring fairly frequently, until they are soft, clear, and just on the edge of caramelizing.
Add flour all at once to the middle of the pan. Carefully and evenly work onions and butter into the flour, stirring constantly, until all onions are completely coated with flour-butter paste.
Cook this mixture, stirring constantly, until it is a medium golden-brown.
Add stock slowly while stirring constantly to avoid lumps.
Add water until soup is just a little thinner than desired consistency (about 1 1/2 to 2 1/2 cups, to taste). Salt lightly.
Cover, and bring just to a boil. Reduce heat to medium.
Simmer, partially covered but vented, about 20 minutes or until soup is desired consistency.
Taste for seasoning and salt to taste.