Unlike eggs en meurette, which are poached in water and finished with a separate meurette sauce, eggs à la bourguignonne are poached directly in red wine for deeper flavor.
Difficulty: [usr 2]
Pour the wine into a saucepan and heat until just about to boil. Crack an egg into a cup and gently slide it into the simmering wine. Repeat with the remaining 3 eggs (if your pan is large enough), using a wooden spoon to carefully draw the whites around the yolks as they poach.
Drain the poached eggs and place them in a deep dish. Keep warm near the oven door while you prepare the sauce.
Melt the butter in another saucepan. Stir in the flour and cook for 3 minutes, stirring constantly, until the roux is smooth and blended.
Pour the lukewarm poaching wine over the roux. Whisk gently over low heat until the sauce thickens and emulsifies. Season with salt and pepper to taste.
Trim and quickly toast the bread slices. Arrange on a serving platter, top each with a poached egg, and spoon the sauce over. Sprinkle with chopped parsley and serve immediately.
For this rustic regional dish and its red wine sauce, a pleasant Passetoutgrains Burgundy is an ideal match.

Source: The Regional Cuisines of France – Burgundy – Editions du Canal.