Heat a large Dutch oven or stockpot over medium high heat.
Add the diced ham, chopped celery, carrots, and sweet onion. Sauté, stirring frequently, for about 5 minutes until the onions are translucent and the ham is slightly browned.
Stir in the halved baby potatoes, sliced leeks, and the bay leaf.
Pour in the dairy free milk and 2 cups of the stock.
Cover the pot and bring the mixture to a boil.
Once boiling, reduce the heat and simmer for about 15 minutes, or until the potatoes are tender and the carrots have softened.
In a small bowl, whisk together the remaining 1 cup of stock with the flour and cornstarch until smooth.
Gradually stir the flour mixture into the soup.
Continue to cook, stirring occasionally, until the broth has thickened to your liking.
Remove the bay leaf and adjust the seasoning with salt and black pepper before serving.