First, make the brine. Bring the water and salt to a boil in a medium pot, stirring until the salt dissolves. Let cool completely. Then, add the muskrat pieces to the water and transfer to the fridge for 24 hours.
When you're ready to cook, preheat the oven to 300 degrees F.
In a Dutch oven or a deep skillet with a lid, add the oil or lard and set over high heat.
Remove the muskrat pieces from the brine, pat dry, season with salt and pepper, then sear until browned on all sides, about 8 minutes.
Add the 2 types of stock straight to the pan. Use a spatula to scrape up any browned bits stuck to the bottom. Bring to a simmer, cover, and transfer to the oven. Cook for 3 hours, or until the muskrat meat easily falls off the bone.
Remove the muskrat pieces. Let them cool, then shred the meat off the bones, discarding the bones when done. Add the shredded meat back to cooking liquid.
In a separate pot, heat the butter over medium heat. Add the flour and whisk until it begins to turn brown (about 5-7 minutes). Then, add the cooking liquid and shredded meat and whisk until it thickens into a thick gravy. Keep hot.
Follow the cooking instructions on the bag of French fries, cooking the fries until they are extra crispy.
Stack the fries into bowls, nestling cheese curds between layers of fries, then pour over the piping hot gravy and serve. Garnish with minced chives.
