Fry bacon in a large skillet set over medium heat until crisp. Remove from the pan and drain on paper towels. Reserve about 3 tablespoons of the drippings in the skillet.
In a medium bowl, whisk together the eggs, sugar, salt, mayonnaise, and cider vinegar. Set aside. Heat the bacon grease in the skillet over medium heat. Whisk in the flour until smooth. Cook, stirring constantly, until the flour is browned, about 10 minutes.
Gradually whisk in the milk so that no lumps form and bring to a boil while stirring constantly. Pour a little hot milk into the egg mixture, whisking constantly; transfer egg mixture to the skillet. Crumble the bacon into the skillet and add the dandelion greens. Cook and stir just until the greens are wilted and heated through.