Place whole baby potatoes in a medium saucepan and cover with cold water by 1 inch. Add 1/2 tsp salt. Bring to a boil over high heat, then reduce to a simmer and cook until potatoes are tender when pierced with a fork, 12–15 minutes depending on size. Drain and let cool slightly, then halve or quarter while warm.

Cook eggs

While potatoes cook, bring a small pot of water to a gentle boil. Add eggs and boil 9 minutes for fully set yolks. Remove eggs to an ice bath for 5 minutes, then peel and quarter.

Blanch green beans

Bring a pot of salted water to a boil. Add trimmed green beans and cook 2–3 minutes until bright green and tender-crisp. Immediately transfer to an ice bath to stop cooking. Drain and pat dry.

Prepare tuna and other components

Drain tuna well, then flake into large chunks with a fork. Halve or quarter tomatoes if using large tomatoes; if using cherry tomatoes, halve them. Thinly slice the shallot. Roughly chop parsley. Keep olives and capers ready.

Assemble salad

On a large platter or in a large salad bowl, arrange mixed greens as a base. Nestle halved potatoes, blanched green beans, quartered eggs, tomatoes, olives, and shallot slices in sections around the platter in the classic Nicoise style. Scatter capers and chopped parsley over the top. Place flaked tuna in the center or in small mounds across the salad.

Dressing

Make the dressing: In a small bowl or jar combine lemon juice, red wine vinegar, Dijon mustard, minced garlic, salt, and pepper. Whisk or shake to combine. Gradually drizzle in the olive oil while whisking (or add oil to jar and shake vigorously) until emulsified. Taste and adjust seasoning with more salt, lemon juice, or pepper as desired.

Dress and serve: Right before serving, drizzle about half of the dressing evenly over the salad, then gently toss or lift components with tongs to coat—be careful not to break eggs or mash potatoes. Serve any remaining dressing on the side. Divide into 4 plates or serve family-style.