Add the full gallon of skim milk, the vanilla bean, and the vanilla bean caviar to a large, stainless steel or enameled pot with a nice, thick, heavy bottom. Slowly bring the milk to a steady simmer over a medium-high burner, stirring frequently to prevent scalding on the bottom of the pan until it reaches 185°F-190°F; about 15 to 20 minutes.
If it does scald, take care not to stir the scalded bits into the rest of the milk. As soon as it hits the target temperature, remove the pan from the burner and allow it to cool to 110°F. Whisk together the Skyr or Siggi's and 1 cup of the 110°F milk until perfectly smooth. Pour that into the pot and stir until fully incorporated.
Use a small whisk to combine the rennet and cool water then immediately stir that into the pot until fully incorporated; about 1 minute. Put the lid onto the pan. Double up a thick bath towel and lay it over the pot. Put the pot in a warm, draft-free place or simply put it lidded pan into an empty oven with the light on for about 12 hours.
Now you have options. You can line a colander with a double thickness of cheesecloth, use a large nut milk bag, or sew a bag of muslin with straps at the top. Spoon the skyr curds into whichever of those you choose, removing the vanilla bean as you go. You do want to spoon and not pour the curd as it is delicate enough that pouring it could break it. Let the cheesecloth rest int he colander or suspend it and allow it to drip over a bowl. You want this place to be rather cool, so a mudroom, refrigerator, or cool room is your best choice. You let this drip for 4 to 8 hours.