Dice the ham. Peel and Dice Carrots. Mince garlic. Dice the potatoes (keep in cold water if doing this in advance to prevent browning). Slice and rinse leeks in cold water to remove any dirt or sand (see reference images and details in the post).
Measure out your Chicken Broth, as well as half and half (or milk).
To a large pot or large frying pan, add the diced carrots and diced potatoes along with enough water just to cover the veggies. Bring to a boil, then cook for about 5 minutes - or until fork tender. Then strain the carrots and potatoes.
To the same large pot or pan over Medium-High heat, add the olive oil, garlic, and sliced leeks. Stir to coat with oil, then add the drained carrots and potatoes. Mix to combine.
Next, add the flour and stir to combine and coat the veggies. Add the broth/stock slowly stirring as you add so that it mixes smoothly with the flour. Turn the heat to a simmer. Once the sauce is starting to thicken (about 3-4 minutes) add the Ham, Dijon mustard, Thyme, Parsley, and half and half (or milk). Stir to combine. Taste for seasoning and add a pinch of salt and black pepper as needed.
Pour the filling of the pie into a PIE DISH and let cool, so it is not steaming, about 30 minutes to overnight in the fridge.