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Season the pork loin all over with salt and pepper. In a large skillet over medium high heat, heat the avocado oil until shimmering. Add the pork roast and brown on all sides, particularly any fatty sections. Place in a slow cooker (5 quarts or larger).
Add the garlic to the pan and cook until fragrant, about 30 seconds. Add the rosemary and stir to combine. Stir in the white wine and scrape up any browned bits, then bring to a simmer. Whisk in the mustard until well combined.
Pour the pan juices over the pork loin and set the slow cooker on high for 3 to 4 hours, or low for 6 to 8 hours. The internal temperature of the pork should reach at least 145F.
Slice the pork thinly and drizzle with the sauce at the bottom of the pot. If you want your sauce a bit thicker, try whisking in about 1/4 to 1/2 tsp of glucomannan.
You can also give the pork loin a last minute browning under your broiler (no more than about 2 to 4 minutes) if you like. I found it didn't need it.