In a large pot, melt the butter over medium heat. Once melted, add the chopped onion and minced garlic. Sauté for about 5 minutes, stirring occasionally, until the onion becomes translucent and slightly golden.

Add the roughly chopped zucchini to the pot. Cook for another 5-7 minutes, stirring frequently. You want the zucchini to soften slightly and develop some color.

Sprinkle the flour over the vegetables and stir constantly for about 1 minute. This will create a roux that will help thicken your soup. Make sure the flour is well incorporated and there are no visible clumps.

Gradually pour in the chicken broth, stirring continuously to prevent lumps from forming. Bring the mixture to a gentle boil, then reduce the heat and let it simmer for about 15 minutes, or until the zucchini is very tender when pierced with a fork.

Remove the pot from the heat. Using an immersion blender, carefully blend the soup until smooth. If you don't have an immersion blender, you can transfer the soup in batches to a regular blender, being cautious with the hot liquid.

Once the soup is smooth, return the pot to low heat and stir in the skim milk. Heat gently for about 2-3 minutes, stirring occasionally. Be careful not to let the soup boil at this stage to prevent the milk from curdling.

Taste the soup and adjust the seasoning with salt and pepper as needed. Remember, the chicken broth already contains some salt, so add gradually and taste as you go.

Serve the soup hot. If desired, garnish with a sprinkle of grated Parmesan cheese, a few croutons, or a dollop of low-fat yogurt for added flavor and texture.