1. Heat butter in a large pot or Dutch oven over medium heat. Add the leeks, onions, garlic, and thyme sprigs (you’ll fish them out later), and season with a good pinch of kosher salt (affiliate link), and several grinds of pepper. Sauté for about 10 minutes, stirring often, until softened.
   
2. Stir in the white wine vinegar and Dijon, and cook, stirring, for about 30 seconds, and then add the chicken stock, potatoes and oats. Sprinkle (or grate) in the nutmeg. Bring to a boil, reduce the heat, and simmer, uncovered, for 30 minutes until potatoes are completely tender when pierced with a fork.
   
3. Let cool slightly. Pluck out the thyme sprigs, then transfer the soup to a blender. Blend until smooth. Take care when blending the hot soup, it expands and can go all over your kitchen. Place a towel over the lid, just in case, and work in batches if necessary. 
4.  Return the smooth soup to the pot and add the milk. Return to a simmer, season to taste with more salt and pepper.

Crispy Fried Leeks can be purchased in many grocery stores and are a tasty garnish. Completely optional, of course!