Bring the potatoes to room temperature and par-cook: Place the halved baby potatoes in a medium saucepan and cover with cold water by 1 inch; add a generous pinch of salt. Bring to a boil, then simmer for 10–12 minutes until just tender when pierced with a knife but not falling apart. Why: par-cooking gives the potatoes a creamy interior while allowing you to finish them in a hot pan or on the grill to develop flavorful browning without overcooking the chicken.

Drain and cool the potatoes slightly, then toss with 1 tsp (of the reserved) olive oil and a small pinch of salt and pepper. Spread on a sheet pan cut-side down and roast or sear in a hot skillet for 8–10 minutes until golden-brown and a little crisp on the edges. Why: browning (Maillard reaction) adds savory depth and a pleasant textural contrast to the salad.

Season the thin-sliced chicken breasts lightly with salt and cracked pepper. If slices are uneven, pound gently between plastic wrap to uniform thickness (about 4–6 mm). Why: even thickness ensures the chicken cooks quickly and evenly without drying.

Preheat a grill pan or outdoor grill to medium-high. Brush the chicken with the 1 tsp olive oil to prevent sticking and encourage a golden crust. Grill the slices 1.5–2.5 minutes per side (depending on thickness) until just cooked through and grill marks form. Internal temperature should reach 74°C (165°F). Why: quick, high-heat grilling seals the exterior for flavor while thin slices cook fast so they stay tender and juicy.

Rest the chicken on a cutting board for 5 minutes, then slice crosswise into bite-sized ribbons or leave whole for the plate. Why: resting allows juices to redistribute; slicing while warm keeps the texture luscious and integrates better with the salad.

Make the tarragon-lemon Dijon vinaigrette: In a bowl or small jar combine the 8 tsp extra-virgin olive oil, 4 tbsp fresh lemon juice, 2 tsp Dijon mustard, 1 finely grated garlic clove, and 4 tbsp chopped fresh tarragon. Whisk or shake vigorously until emulsified; season with salt and pepper to taste. Why: whisking mustard into the acid before adding oil helps the emulsion form; bright lemon and aromatic tarragon are a classic pairing that cuts through the richness of the oil and chicken.

Assemble the salad: In a large bowl, add the roasted baby potatoes and warm sliced chicken — warm components hold the dressing better — then pour about two-thirds of the vinaigrette over them and toss gently to coat. Add the arugula and halved cherry tomatoes and toss once more (add remaining dressing to taste). Why: dressing warm potatoes and chicken allows flavors to meld; adding most but not all dressing lets each diner adjust, and tossing gently keeps arugula from wilting excessively.

Plate family-style or individually: divide onto 4 plates, finish with a sprinkle of extra chopped tarragon, a few grinds of cracked black pepper, and an optional lemon wedge. Taste and adjust salt if needed. Why: finishing touches heighten aroma and freshness; a lemon wedge lets guests add an extra lift if desired.

Serve immediately while chicken and potatoes are still slightly warm. Why: contrasts between warm protein/potato and cool peppery arugula make the dish most vibrant; this is best eaten the day it’s made for texture and flavor.