Lightly toast the bread. Rub one side of each slice with the garlic and brush lightly with olive oil. Put 1 slice on each of 4 plates.
Put the asparagus in a 12-inch nonstick skillet with 1/2 cup water, the olive oil, and 1/2 tsp. salt. Cover, bring to a boil over medium-high heat, and cook until tender, about 5 minutes.
Meanwhile, crack the eggs into a shallow bowl. When the asparagus is ready, pat dry and divide it among the pieces of toast. Wipe out the skillet with paper towels if wet; then slide the eggs into the hot skillet, sprinkle each with a pinch of salt and pepper, cover, and cook over low heat until the whites are firm but the yolks are still runny, about 2 minutes.
Top each toast with an egg. Garnish with the shaved Pecorino, and serve.