Sauté asparagus in 1 tsp oil in a large skillet until crisp-tender. Set aside
Sauté green onion in 2 tsp oil and 1 Tbsp butter until tender. Add mushrooms & garlic. Cook 4 minutes. Add sherry, stir in cream and salt. Bring to a boil. Cook, stirring 2 minutes until slightly thickened Stir in basil.
Meanwhile, poach the eggs. Fill large skillet with water, add vinegar. Bring to a boil, reduce heat and simmer gently. Break cold eggs, one at a time, into a saucer, holding it close to the surface of the water, slip each egg into water.
Cook, uncovered, until whites are set and yoks are soft, about 4 minutes. With a sotted spoon, lift eggs out of the water.
Spread remaining butter over toast slices. Top each with asparagus, a poached egg and mushroom mixture. Sprinkle with pepper and drizzle with balsamic vinegar.