Step 1

Mash anchovies with a spoon in a small bowl. Add mustard and 2 tablespoons lemon juice. Gradually whisk in 1/2 cup oil. Season with salt and pepper.

Step 2

Cover potatoes with 2 inches water in a pot. Add 1 tablespoon salt. Bring to a boil, then reduce to a simmer and cook until knife-tender, about 12 minutes. Drain. Let stand until cool enough to handle, then halve potatoes.

Step 3

Heat grill to medium-high. Brush salmon lightly with oil, sprinkle with zest and remaining 1 tablespoon lemon juice, and season with salt and pepper. Brush grill grates with oil, then place salmon on grill, skin-side down. Cook until skin is crisp and browned, about 6 minutes a side for medium-rare, 8 minutes a side for medium. Remove from grill.

Step 4

Place a wire rack on grill (or use a vegetable grill basket). Toss snap peas with remaining 2 teaspoons oil, transfer to rack, and grill, tossing frequently with tongs, until charred in spots, 3 to 5 minutes. Remove from grill.

Step 5

Meanwhile, bring a pot of water to a boil. Gently lower eggs into pot; simmer 8 minutes. Drain, then run under cold water to stop cooking; peel and halve.

Step 6

Pour half of dressing into a serving bowl. Add potatoes; toss to coat. Add watercress and toss again. Flake salmon into large pieces; add to bowl. Top with eggs and peas and serve, with remaining dressing on the side.