Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, carrots, and celery. Cook, stirring occasionally, until softened, about 5 to 7 minutes.
Stir in the minced garlic and cook for 1 more minute until fragrant.
Add the cubed chicken to the pot. Season with 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Cook, stirring occasionally, until the chicken is lightly browned on all sides.
Sprinkle the flour over the chicken and vegetables. Stir constantly for 1 minute to cook the flour taste out.
Slowly pour in the chicken broth and milk while stirring to prevent lumps from forming. Scrape any browned bits from the bottom of the pot.
Add the potatoes and bring the soup to a gentle simmer. Reduce the heat to low, cover, and let it cook for 15 to 20 minutes, or until the potatoes are tender when pierced with a fork.
Confirm the chicken is cooked through by checking that its internal temperature reaches 165°F (74°C) on a meat thermometer.
Remove the pot from the heat. Gradually stir in the shredded cheddar cheese until it has completely melted and the soup is smooth.
Taste the soup and add more salt and pepper if needed. Serve warm, garnished with fresh parsley.