Render bacon on medium heat in your soup pot until it is crispy, then set aside. Retain bacon fat in pot.
Add the chopped leeks, celery, carrots, and tomatoes to the soup pot and saute on medium or medium-low for a couple of minutes. Then add the fresh thyme, salt, pepper, dried tarragon, bay leaf and clam juice. Continue cooking until vegetables are softened. While vegetables are cooking, get a small pot and melt butter.
Once the butter is melted, add the corn starch and mix well. Cook for a few minutes before adding to the soup pot.
Add the cans of clams in their juice, milk and heavy cream to the pot along with the potatoes and the reserved bacon. Cook on medium-low to low until potatoes are cooked through. Approximately 20 - 30 minutes.
Taste the broth and adjust for seasoning, adding salt and pepper to taste.