Dice the onion and mince the garlic, then set aside.
Place the chicken breasts in the large heavy-bottomed pot and cover with water. Bring to a gentle boil and cook until just done, about 15 minutes. Remove, let cool slightly, then shred with two forks.
In the same pot, add a splash of oil and sauté the diced onion and minced garlic over medium heat until fragrant and golden, about 3 minutes. Stir occasionally to prevent burning.
Add the diced carrots and celery to the pot, stirring to combine. Cook for another 5 minutes until the vegetables start to soften and release aroma.
Pour in the chicken broth, then add the shredded chicken back into the pot. Bring everything to a gentle simmer and cook for 20 minutes until the vegetables are tender.
Stir in the heavy cream and shredded cheddar cheese, then reduce the heat to low. Continue stirring until the cheese melts completely and the soup becomes velvety, about 5 minutes.
Season the soup with salt and pepper to taste. Squeeze in the lemon juice for brightness and stir well.
Garnish with chopped fresh herbs if desired, then ladle into bowls and serve hot.
