Combine 3 tbsp of arrowroot starch and salt and pepper in a shallow bowl. Pat the salmon filets dry, and working with one at a time, toss with the arrowroot starch to coat. Set aside.
Using a large, deep pan, melt 1 tbsp ghee over medium heat. Once the ghee is melted and shimmering, add the salmon to the pan skin side down. Sear the salmon for about 4 minutes on each side or until crisp and cooked through. Set aside on a plate and cover with foil to keep warm.
Add the white wine to the pan and scrape with a wooden spoon to remove any burnt bits from the bottom.
Add another tablespoon of ghee to the pan. Once melted, add the garlic and saute for 2-3 minutes or until lightly fragrant.
Whisk 1 tsp of arrowroot with the broth and pour into the pan along with the lemon juice. Bring to a simmer for 4-5 minutes to allow to thicken. Add the capers, parsley, and lemon slices and stir to combine. Reduce the heat.
Add the salmon back to the pan and spoon the sauce over the filets. Serve fresh with a side of gluten-free pasta and vegetables of your choice.