In a medium saucepan, combine the wild rice, butter and 1 3/4 cups water. Bring to a boil then lower heat to simmer, cover the saucepan and cook for 45 minutes.
Add the olive oil to a large stock pot over medium heat. Add the onion and saute for 2 minutes. Add garlic, broccoli and carrots and cook for 5 minutes or until softened. Add the chicken stock and simmer for 5 minutes.
Meanwhile, heat a separate sauce pan over medium heat. Melt the butter then whisk in the flour, salt and pepper. Cook for 1 to 2 minutes to cook out the flour taste. Slowly add half the milk, whisking as you pour. Let it thicken slightly then add the remaining milk. Cook, stirring often, until the mixture has thickened. Remove from the heat and stir in the shredded cheddar.
Add the cheese sauce to the stock mixture and whisk thoroughly. Stir in the shredded chicken and cooked rice. Allow to simmer for 10 minutes to heat through the chicken and rice and thicken the soup a bit.