Heat the olive oil in a large heavy-bottomed pot or Dutch oven over medium heat.
Add the diced onion, carrots, and celery to the pot, sautéing for about 5 to 7 minutes until the vegetables are softened.
Stir in the minced garlic and cook for 1 minute until fragrant.
Pour in the diced tomatoes with their juices, white beans, diced potatoes, rinsed quinoa, and vegetable broth.
Bring the soup to a gentle boil, then reduce the heat to low, cover, and simmer for 20 to 25 minutes, or until the potatoes and quinoa are tender.
Stir in the chopped kale and continue to simmer uncovered for 3 to 5 minutes until the greens are wilted.
Remove the pot from the heat, stir in the fresh lemon juice, and ladle into bowls.
Garnish each serving with freshly grated Parmesan cheese and serve immediately.