(This is an expansion of my comment -- both more general and more specific)
In many recipes that use milk, the milk is just there as a liquid. Replacing it with a suitably-flavoured liquid is often appropriate (though in the presence of other dairy ingredients be cautious before adding anything too acidic).
You don't give any idea of the quantity but assuming it's small you could try apple juice/cider (a nice pairing with pork if not too sweet). Now when I say cider I mean the alcholic sort ("hard cider"?) -- it's less sweet than cloudy apple juice. If you also want to avoid alcohol, a variation is juice with a few drops of cider vinegar. The flavour is different but can be good with pork. With other meats white wine can work.
In some cases adding (more) beaten egg in place of the milk might work, but some things would become too firm. Given that there's rather a lot of milk in this recipe, replacing it with egg would make change both the texture and the flavour too much.
You could quite possibly use a non-dairy milk (almond/soya/rice) though these won't always substitute for real milk. Again, when they will work is when the milk is being just a liquid. Long, gentle cooking of recipes with milk in often means that non-dairy milks won't work so well. You'd also need to consider whether the flavours work, in particular sweetness.