Place diced potatoes in a medium pot and cover with cold salted water. Bring to a boil, then reduce to a simmer and cook until tender, 12–15 minutes. Drain well and return to the pot to steam-dry for 1–2 minutes.

Mash the potatoes until mostly smooth, leaving a little texture. Let cool slightly (warm, not hot).

While potatoes cook, blanch peas in boiling water for 1 minute then drain and cool. If using frozen, ensure thawed. Squeeze excess water from grated carrot if very wet.

Combine mashed potatoes, grated carrot, peas, sliced green onion, chopped parsley, mayonnaise, Dijon mustard, lemon juice, salt, and black pepper in a large bowl. Fold in chopped hard-boiled eggs if using. Mix until evenly distributed; the mixture should hold together when squeezed. Adjust salt and lemon to taste.

Chill the mixture in the refrigerator for 20–30 minutes to firm up (this makes shaping easier).

Breading & Frying

Set up a breading station: shallow bowls with flour, beaten eggs, and breadcrumbs. Season flour with a pinch of salt and pepper.

Divide the chilled potato-salad mixture into 8 equal portions (about 2–3 tablespoons each). Shape each portion into a compact oval or round croquette, pressing firmly to remove air pockets.

Dredge each croquette first in flour (shake off excess), then dip in beaten egg, and finally coat evenly with breadcrumbs. Press breadcrumbs gently so they adhere. For a crisper crust, double-coat: dip again into egg and breadcrumbs.

Pour vegetable oil into a large skillet to reach about 1/8–1/4-inch depth and heat over medium. Test oil by dropping a single breadcrumb; it should sizzle immediately but not smoke.

Fry croquettes in batches (do not overcrowd) for 2–3 minutes per side, until golden brown and heated through. Use a spatula to turn carefully. If color is darkening too quickly, reduce heat to medium-low.

Transfer fried croquettes to a wire rack or paper towel-lined plate to drain. Keep warm in a low oven (200°F / 95°C) if making multiple batches.

Salad Garnish & Serving

Toss mixed salad greens, halved cherry tomatoes, and cucumber slices with olive oil, red wine vinegar, salt, and black pepper in a medium bowl.

Arrange a bed of dressed salad greens on each plate (divide into 4 portions). Place 2 croquettes on top of the salad per serving.

Garnish with a lemon wedge and extra parsley if desired. Serve immediately while croquettes are warm.