How to Make It
Preheat the oven to 400°. On a baking sheet, brush the peppers with olive oil and roast for 20 minutes, turning once, until lightly browned and softened. Transfer the peppers to a bowl, cover with plastic wrap and let cool for 10 minutes.
Meanwhile, in a medium skillet, heat 2 tablespoons of the olive oil. Add the mushrooms and cook over moderately high heat, stirring, until lightly browned, 4 minutes. Stir in the shallot, garlic and marjoram and cook until fragrant, 2 minutes. Season with salt and pepper and keep warm.
Peel, core and seed the peppers. Transfer the peppers to a blender and puree. With the machine on, add the remaining 3 tablespoons of oil and the hot sauce and puree. Season with salt and pepper.
Bring a large saucepan filled with 3 inches of water to a simmer. Crack each egg into a cup, then slide it into the water. Poach the eggs over low heat until the whites are set and the yolks are runny, 4 minutes. Using a slotted spoon, lift the eggs out of the water and blot them dry.
Spoon the pepper puree onto plates and top with the mushrooms. Set the eggs on the mushrooms, season lightly with salt and pepper and serve.
One serving 294 cal, 15 gm carb, 23 gm fat, 4 gm sat fat, 10 gm protein, 1 gm fiber.