Preheat the oven to 400°.
Heat a large skillet over medium high heat. Add the oil. When the oil is shimmering, add the mushrooms and season with salt and pepper. Cover and cook over moderate heat, stirring a few times, until softened, 4 minutes.
Add the shallot and cook, stirring occasionally, until the shallot is softened and the mushrooms are browned, about 3 minutes longer.
Add the sherry and cook until almost evaporated, 1 minute. Season with salt and pepper. Remove from the heat, cover and set aside.
Arrange the bread slices on a large rimmed baking sheet and brush with olive oil. Bake for about 6 minutes, until toasted. Transfer the toasts to plates.
In a large, nonstick skillet, melt the butter over moderate heat. Cook the eggs, sunny-side up, until the whites are firm and the yolks runny, about 5 minutes.
Spoon the mushroom mixture onto the toasts and top with the fried eggs. Garnish with the parsley and serve.