Preheat your oven to 425°F and place the halved potatoes on a baking sheet. Drizzle generously with olive oil, season with salt and pepper, and roast cut-side down for 15 minutes.
Arrange the red spring onion slices over the potatoes and continue roasting for 25 minutes until golden and tender. Let them cool for about 10 minutes on the sheet pan.
In a large bowl, combine the arugula, radishes, and green spring onion stems. This creates a fresh, crisp layer that complements the warm potatoes.
In a food processor, pulse arugula, basil, chives, garlic, pine nuts, pecorino, lemon zest, lemon juice, and honey until finely chopped. Stir in olive oil at the end for a textured, vibrant pesto.
Add the roasted potatoes and onions to the salad bowl. Drizzle with pesto and toss gently to coat everything evenly. Serve warm or at room temperature with extra black pepper if desired.