The day before, make a brine by combining 3 tablespoons of salt and 3 cups of water. Stir until salt dissolves. Cut the muskrat into 8 pieces, then submerge them in the brine. Cover and transfer to the fridge for 12-24 hours.
Once ready to cook, remove the meat from the brine and pat it dry with paper towel.
Add the sesame and lard/vegetable oil to a skillet over medium heat. Add the garlic, ginger, and chili slices and cook, stirring, for about 3 minutes. Add the muskrat pieces, flipping the aromatics on top of the meat if possible. Cook for 2 minutes, then flip and cook for another 2 minutes. Add the wine, water, soy sauces, and sugar and mix well, bringing to a boil. Reduce to a low simmer and cover the skillet.
Simmer for 30 minutes, checking intermittently so that nothing burns. Remove the lid and reduce the liquid until it thickly coats the meat, stirring constantly. Once the liquid is thick, take it off the heat and add the basil leaves, stirring them in and letting them wilt. Serve with jasmine rice. Enjoy!