Preheat oven to 400°. Place half of chickpeas on a rimmed baking sheet, drizzle with 2 Tbsp. oil, and toss to coat. Season with salt and pepper. Roast until chickpeas are golden brown and crispy, 20–23 minutes. Let cool; set aside.
Whisk remaining 3 Tbsp. oil, 1 Tbsp. lemon juice, dried mint, and vinegar in a small bowl. Season vinaigrette with salt, pepper, and more lemon juice, if desired.
Combine remaining chickpeas, arugula, fresh mint, and onion in a large bowl. Drizzle vinaigrette over and season with salt and pepper; gently toss to coat. Divide salad among plates or bowls. Garnish with reserved roasted chickpeas and feta.