How to Make It
Lightly oil an 8-inch-square waffle iron and preheat it. In a medium bowl, whisk the flour with the sugar, baking powder, salt and pepper. In another bowl, combine the butter, shallots and rosemary; whisk in the eggs and then the buttermilk. Gradually stir the wet ingredients into the flour mixture.
Pour one-third of the batter into the waffle iron and bake until browned, about 8 minutes. Set the waffle aside and bake the remaining batter in 2 batches.
In a large skillet, heat the olive oil. Add the shallots and garlic and cook over moderate heat, stirring frequently, until softened but not browned, about 3 minutes. Add the mushrooms, sherry, parsley and thyme and season with salt and pepper. Cover and simmer over moderately high heat for 5 minutes. Uncover and add the cream. Cook, stirring, until the mushrooms are tender and the sauce is thickened, about 10 minutes. Season with salt and pepper and keep warm.
Bring a large skillet of water to a boil and add the vinegar. Break 4 of the eggs into the water, 1 at a time. Simmer gently over moderate heat until the whites are firm and the yolks soft, about 3 minutes. Using a slotted spoon, transfer the eggs to a paper towel-lined platter. Repeat with the remaining eggs.
Meanwhile, cut each waffle into 4 squares and toast until crisp. Set 2 squares on each of 4 warmed plates. Arrange 2 eggs on each plate and spoon the mushrooms on top. Pass the remaining waffles separately.