Heat a large heavy-bottomed pot over medium heat and add two tablespoons of olive oil. When the oil shimmers and starts to smell fragrant, add the diced onion and chopped carrots. Cook, stirring occasionally, until the vegetables are soft and translucent, about 8 minutes, and you hear a gentle sizzle.
Add the minced garlic to the pot and cook for about 1 minute, stirring constantly, until fragrant and golden at the edges. Be careful not to burn it.
Pour in the chicken broth and bring the mixture to a gentle simmer. Once bubbling, add the shredded cooked chicken and small pasta shapes. Stir to combine, and let it simmer uncovered for about 10 minutes, or until the pasta is tender and the greens are starting to wilt.
Add the chopped greens to the pot and cook for an additional 2-3 minutes until they are tender and wilted, creating a vibrant splash of color in the soup.
Taste the soup and season with salt and pepper as needed. Squeeze fresh lemon juice into the pot to brighten and lift the flavors, stirring well.
Serve the soup hot, ladled into bowls, with an extra squeeze of lemon and fresh herbs if desired. Enjoy the comforting warmth and satisfying textures in every spoonful.