Heat the olive oil in a large pot over medium heat. Add the onion and cook until it’s translucent and flirting with golden. This is your flavor base, so don’t rush it.
Stir in the garlic and cook for about 30 seconds until it smells amazing. If you burn it, pretend it’s caramelized and move on—kidding, keep an eye on it.
Add the carrots and celery. Sauté for 3–4 minutes to soften a touch. You want a little bite left; texture is happiness.
If you’re using flour for thickness, sprinkle it in now and stir to coat the veggies. Cook for 1 minute to remove raw flour taste.
Pour in the chicken broth and milk. Scrape the bottom to release any tasty browned bits. Bring to a gentle simmer.
Add the shredded chicken, thyme, and a pinch of salt and pepper. Let everything simmer for 6–8 minutes, so flavors mingle like old friends at a reunion.
Stir in the cream and heat through. Taste and adjust seasoning. If it’s too thick, splash in a little more broth or milk until you’re happy with the sauce-to-chicken ratio.
Serve hot with a sprinkle of parsley or chives. Optional: a crack of black pepper for drama. Enjoy the cozy, creamy goodness.