Heat the butter in a pot over medium heat. Sauté the onion, carrots, celery until beginning to soften (about 4 minutes).

Add the ham and potatoes, cook for 2 minutes, add salt and pepper, then add the garlic and sauté until fragrant (about 30 seconds).

Mix the flour through and cook for 2 minutes.

Stir in stock and bouillon, mixing all ingredients together. Increase heat and bring to a boil until potatoes are 'just' fork tender, about 10-12 minutes.

Reduce heat to medium-low, add the milk and stir over the heat until thickened (about 5 minutes).

Taste test and season with salt and pepper, if desired.

Serve warm.