Fry the bacon in a large skillet until crisp, then remove. Leave the fat in the skillet.
Salt and pepper the chicken quarters, then dust lightly with flour. Raise the heat to high and brown the chicken pieces in the bacon fat on all sides. Remove the chicken pieces and keep warm.
In the same pan cook the ham, green onions, and yellow onions until the latter turn translucent. Add mushrooms, wine, Worcestershire, and Tabasco, and bring it up to a boil. After a minute, lower to a simmer.
In a separate skillet, fry the potatoes in 375-degree oil until very lightly browned. Drain them well and add to the ham, onions, etc. You now have the bonne femme garnish.
Continue simmering sauce until all of the liquid is absorbed; lightly stir to distribute ingredients. Remove from heat.
Heat the butter in a small saucepan until it starts bubbling. Lower the heat, skim the foam off, and add the garlic. Cook the garlic in the hot butter for about a minute.
Put the chicken pieces in a broiling pan. Put the pan into a preheated 400-degree oven and cook for seven to ten minutes. Turn the pieces, and cook them another 5-7 minutes.
Spoon the bonne femme garnish over and between the chicken pieces. Crumble the bacon over the top. Continue cooking until the juices run clear when the thigh is pierced. Serve the bonne femme garnish over the top of the chicken pieces.