To a large pot over medium heat, add 2 tablespoons of butter. Once the butter has melted, add onions and carrots. Cook until softened (3-5 minutes).
Add garlic, salt, and pepper. Cook for an additional minute.
Add potatoes. Pour in chicken broth. Cover and simmer for 12-15 minutes, or until potatoes are fork-tender.
In a separate skillet over medium-low heat, melt the remaining butter. Once melted, sprinkle in the flour and whisk to combine. Cook until lightly browned (about 1-2 minutes).
Add the sour cream, and stir until fully combined.
Add the sour cream mixture to the potato mixture. Stir to combine.
Carefully, transfer ⅓ of the soup to a bowl. Using an immersion blender, blend until smooth.
Return the blended soup back to the pot.
Add ham. Cook until heated through (about 5 minutes).
Serve hot, garnished with parsley.