Remove cap, stem and gills from portobello mushroom. Slice mushroom into thin, bite-size strips (julienne). Slice onion into thin, bite-size strips (julienne).
In a medium skillet, melt butter over medium heat. Add mushroom and onion; cook and stir for 5 to 8 minutes or until onion is tender but not brown; drain well. Set aside.
Lightly grease a 10-inch skillet. Half fill the skillet with water (a splash of white vinegar will help set the whites). Bring water to boiling; reduce heat to simmer (bubbles should begin to break the surface of the water). Break one of the eggs into a 1-cup measuring cup with a handle. Holding the lip of the cup as close to the water as possible, carefully slide egg into simmering water, taking care to not break the egg. Repeat with remaining eggs, allowing each egg an equal amount of space.
Simmer eggs, uncovered, for 3 to 4 minutes or until the whites are completely set and yolks begin to thicken but are not hard. Remove eggs with a slotted spoon and place them in a large pan of warm water to keep them warm.
Prepare the Hollandaise Sauce.
Meanwhile, place English muffin halves, cut side up, on a lightly greased or foil-lined baking sheet. Broil 3 to 4 inches from the heat about 2 minutes or until toasted. Remove from oven.
Spoon mushroom-onion mixture on muffin halves. Top with roasted pepper strips and feta cheese. Return to broiler. Broil 3 to 4 inches from the heat for 1 to 2 minutes or until cheese is softened and lightly browned.
To serve, gently place a well-drained egg on top of each feta-topped muffin half. Spoon about 2 tablespoons of the Hollandaise Sauce over each egg. Sprinkle eggs with capers. Makes 4 servings.
Cut softened butter into thirds. In the top of a double boiler, combine beaten egg yolks, water, lemon juice, salt and white pepper. Add a piece of the butter. Place over boiling water (upper pan should not touch water). Cook, stirring rapidly with a whisk, until butter melts and sauce begins to thicken. Add the remaining butter, a piece at a time, stirring constantly until melted. Continue to cook and stir until sauce thickens (about 2 minutes more). Immediately remove from heat. If sauce is too thick or curdles, immediately whisk in 1 to 2 tablespoons hot water. Makes 3/4 cup sauce.