Heat a large pot over medium heat and add olive oil. Once shimmering, add the chopped onion and cook until soft and translucent, about 3-4 minutes, filling your kitchen with a gentle aroma.
Add the minced garlic to the pot and cook for another minute, stirring constantly until fragrant and slightly golden, releasing a warm, savory scent.
Pour in the vegetable broth and crushed tomatoes, stirring to combine. Bring the mixture to a gentle simmer, watching for bubbles to form around the edges of the pot.
Add the pasta to the simmering broth, stirring to prevent sticking. Cook until the pasta is just tender, about 8-10 minutes, until you see it plump up with a slightly al dente bite.
Stir in the chopped spinach, allowing it to wilt and release a vibrant green color, adding freshness and a touch of earthiness to the broth.
Lower the heat and add the shredded mozzarella and grated Parmesan cheeses, stirring continuously until the cheese melts smoothly into the broth, creating a creamy, cheesy layer.
Season the soup with salt and freshly ground pepper to taste, adjusting the flavors until balanced and inviting, with a rich, cheesy aroma.
Once everything is heated through and the cheese has fully melted, turn off the heat and let the soup sit for a minute to thicken slightly, silken and bubbly on top.
Serve the hot, cheesy lasagna-inspired soup in bowls, garnished with a sprinkle of additional Parmesan or fresh herbs if desired, for a cozy, comforting meal.