Heat the oil: In a large pot, heat the olive oil over medium heat. Add the chopped onion and minced garlic, sautéing for 3-5 minutes until softened and fragrant.
Cook the vegetables: Add the chopped carrots and diced potatoes to the pot. Stir to combine and cook for an additional 5 minutes.
Add the broth: Pour in the vegetable broth (or chicken broth) and bring to a boil. Reduce the heat and let the soup simmer for about 20-25 minutes, until the potatoes are fork-tender.
Season and add spinach: Stir in the paprika, salt, pepper, and lemon juice. Add the chopped spinach and simmer for an additional 5 minutes until the spinach is wilted.
Serve: Ladle the soup into bowls and top with fresh herbs, a dollop of sour cream, or crispy croutons, if desired.