Warm the olive oil in a large pot or Dutch oven over medium heat, then add the onion, carrots, and celery and cook for about 10 minutes, stirring now and then. The vegetables should soften and smell sweet while still holding a little firmness, not turn deeply brown.

Stir in the garlic, thyme, oregano, crushed red pepper, 1 teaspoon salt, or 2 teaspoons if you are using low-sodium broth, and 1 teaspoon black pepper, then cook for about 1 minute. Stop as soon as the garlic smells fragrant and the herbs bloom in the oil.

Add the diced potatoes and tomato paste and cook for 2 to 3 minutes, stirring often to coat everything well. The tomato paste is ready when it darkens slightly and you catch that caramelized aroma from the bottom of the pot.

Pour in the vegetable broth and diced tomatoes with their juices, bring the pot to a boil over medium-high heat, then lower the heat and simmer partially covered for 20 to 25 minutes. The potatoes should be fork tender with just a little resistance left in the center before they fully give way.

Mix in the green beans, corn, and peas, return the soup to a simmer, and cook for 3 to 5 minutes more. The green beans should lose their raw edge but still keep shape and color.

Take the pot off the heat and stir in the spinach, parsley, and red wine vinegar, then taste and adjust with more salt and pepper if needed. The spinach should turn a bright deep green and wilt quickly into the hot broth without overcooking.