Season the chicken cutlets on both sides with the salt and pepper and set aside.

Pour the arrowroot starch on a large plate or in a wide bowl. Lightly dredge each individual cutlet in the arrowroot flour until evenly coated, then shake off any excess. Place the dredged cutlets on a clean plate and continue until all are complete.

Heat the oil in a large skillet over medium-high heat. Working in batches so as to not overcrowd the skillet, carefully add the cutlets and cook until golden brown on both sides, 3 to 4 minutes per side. The chicken does not need to be completely cooked through, just golden brown. Transfer to a parchment-lined plate. Repeat with the remaining chicken, adding more oil to the pan if necessary.

Reduce the heat to low, add the ghee to the skillet, and swirl to evenly coat the bottom of the pan. Add the garlic and cook until fragrant, stirring to prevent burning, about 30 seconds. Stir in the capers, chicken broth, and lemon juice. Increase the heat to a simmer. Nestle the chicken into the sauce and cook, uncovered and stirring occasionally, until the sauce has thickened and the chicken is tender, about 15 minutes. Taste and adjust the seasoning with salt and pepper, if desired. Garnish with the parsley and serve.