Place a Dutch oven or other large pot with a lid over medium heat. Add fat and when melted, add onion, carrot, celery and leeks. Saute for 5-7 minutes, stirring occasionally until onions start to soften.
Add garlic, stir and cook an additional 30 seconds.
Add potatoes, broth and thyme. Bring soup just to a boil then reduce heat, cover and simmer until potatoes and carrots are tender - about 30 minutes, depending on how large they are and how vigorous the simmer.
When vegetables are tender, insert an immersion blender into the soup on one side of the pot and process until creamy. Stir to mix the part you just pureed into the other half of the soup (you can also remove ½ of the soup and process it in a blender or food processor then return it to the pan).
Add diced ham and kale continue to heat until ham is warm and kale is wilted. Taste and season with salt and pepper as desired. Serve.
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