In a stand mixer, cream together the butter and grated cheese until smooth. It shouldn't take long.
Mix together the spices with the flour, then add it to the mixer. Mix on low-speed until mostly incorporated — it's okay to be a little bit crumbly.
Add milk, one tablespoon at a time, until the dough comes together. It should not be sticky, but should hold together in a ball.
Form the dough into a disk and wrap in plastic wrap. Chill for 30+ minutes.
When the dough has chilled, preheat the oven to 400 F.
On a lightly floured surface, roll the dough out very thin — ⅛" or less. Cut it into your desired shape, sprinkle salt all over, and bake on a parchment-lined cookie sheet for 10-11 minutes.
Let the crackers cool at least 5 minutes before eating.
Recipe by The Kitchen Paper at http://c02.ddd.mwp.accessdomain.com/spiced-cheese-crackers/