Step 1

Whisk lemon juice, egg yolk, garlic, Worcestershire, mustard, anchovies, ½ teaspoon salt, and ¼ teaspoon pepper together in bowl. Whisk in ½ cup oil until smooth. Whisk in grated Parmesan; set aside.

Step 2

FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.

Step 3

FOR A GAS GRILL: Turn all burners to high; cover; and heat grill until hot, about 15 minutes. Leave all burners on high.

Step 4

Clean and oil cooking grate. Brush bread slices all over with remaining 3 tablespoons oil and sprinkle with remaining ¼ teaspoon salt and remaining ¼ teaspoon pepper. Grill bread, uncovered, until browned, about 1 minute per side. Transfer to large plate.

Step 5

Whisk dressing to recombine and toss asparagus with ⅓ cup dressing on rimmed baking sheet until asparagus is evenly coated. Arrange asparagus on grill perpendicular to grill grates. Grill (covered if using gas), turning occasionally, until asparagus is char-streaked and tender, 2 to 5 minutes. Transfer to serving platter.

Step 6

Tear bread into bite-size pieces. Drizzle asparagus with remaining dressing. Top with shredded Parmesan and torn bread. Serve.