With the rack in the middle position, preheat the oven’s broiler. Line a baking sheet with parchment paper.
In a food processor, chop the pine nuts. Transfer to a plate.
In a microwave, melt 30 ml (2 tablespoons) of apricot jam and brush one side of the cutlets with the jam. Season with salt and pepper. Press the jam-covered side in the pine nuts.
In a large skillet, brown the cutlets, nut side up, in the oil. Place on the baking sheet and bake for about 2 minutes or until the chicken is cooked. Keep an eye on the meat while cooking because pine nuts burn quickly.
Meanwhile, in the same skillet, brown the onion. Add oil, if needed. Add the garlic and cook for 1 minute. Add the broth, the remaining jam, and the mustard. Bring to a boil and reduce for 2 minutes or until the sauce is syrupy. Remove from the heat and add the butter with a whisk. Season with salt and pepper.