Unlike in a classic minestrone, the vegetables in this dish are cooked quickly to preserve their bright flavor.
1⁄2 cup packed basil leaves
1⁄4 cup extra-virgin olive oil, plus more for drizzling
2 tbsp. minced fresh flat-leaf parsley
4 cloves garlic
1⁄2 medium onion, cut into chunks
8 oz. red new potatoes, cut into 1⁄2" cubes
3 stalks celery, minced
2 medium carrots, minced
2 plum tomatoes, cored and minced
Kosher salt, to taste
3 oz. spinach, trimmed and rinsed (about 2 loosely packed cups)
1 1⁄2 cups canned cannellini beans, rinsed
1 cup fresh or frozen green peas
1⁄2 small head frisee, leaves cut into bite-size pieces (about 2 cups)
Freshly ground black pepper, to taste
Freshly grated Grana Padano or parmesan, for serving
Place half the basil, 2 tbsp. oil, parsley, garlic, and onions in the bowl of a food processor and process until slightly chunky. Heat remaining oil in an 8-qt. pot over medium-high heat and add herb-garlic mixture. Cook, stirring often, until no liquid remains, about 5 minutes. Add potatoes, celery, carrots, and tomatoes. Cook, stirring often, until vegetables are golden brown, about 6 minutes. Add salt and 4 cups water and bring to a boil. Reduce heat to medium-low; cover and cook, stirring occasionally, until vegetables are tender, about 20 minutes.
Stir in spinach, beans, peas, and frisee and cook until greens are wilted and just tender, about 10 minutes; season with salt and pepper and stir in remaining basil. To serve, ladle soup into bowls, sprinkle with Grana Padano, and drizzle with oil.