Heat butter or oil in a large heavy-bottomed pot over medium heat. Add diced onion and minced garlic, sautéing until fragrant and golden, about 3 minutes.
Add diced carrots and celery to the pot, stirring to combine. Cook for about 5 minutes until vegetables start to soften and release their aroma.
Pour in the chicken broth and bring the mixture to a gentle simmer. Add the cooked and shredded chicken, stirring to distribute evenly. Let it simmer for 20 minutes until the vegetables are tender.
Stir in the heavy cream and shredded cheddar cheese, stirring constantly to prevent lumps and ensure a smooth, velvety texture. Lower the heat to medium-low and cook for another 5 minutes until the soup thickens slightly.
Season the soup with salt, pepper, and a squeeze of fresh lemon juice to brighten the flavors. Taste and adjust the seasoning as needed.
Serve the soup hot, garnished with chopped fresh parsley or thyme for a burst of freshness and color.