For the lamb chops: Lay chops out on a platter and season all over with pepper to taste. Mix cayenne and oil together, rub all over chops, then scatter bay leaves and savory on top. Cover with plastic wrap and set aside, at room temperature, to let marinate for 2–3 hours.
Preheat a charcoal grill. Season both sides of chops with salt to taste and grill over hot coals, turning and moving chops around grill to prevent flare-ups, until well browned on each side, 3–4 minutes per side for medium rare. Set aside to let rest for 10 minutes before serving.
For the potato pancake: Grate potatoes on the large holes of a box grater. Working with small handfuls at a time, squeeze out moisture from potatoes and transfer potatoes to a medium bowl. Add garlic, parsley, and salt and pepper to taste and mix well.
Heat half the butter and half the oil together in a medium nonstick skillet over medium heat. Spread potatoes in bottom of skillet, forming a loose, even layer with ragged edges. Cook pancake, gently pressing on potatoes with the back of a spatula once or twice and shaking skillet over heat occasionally, until a pale golden crust forms on the bottom, 6–7 minutes. Carefully invert pancake onto a large plate. Heat remaining butter and oil together in same skillet. Return pancake to skillet, raw side down, and cook, shaking skillet occasionally, until pale golden on second side, 6–7 minutes. Invert pancake again, return to skillet, and cook until crust is a little more golden, about 2 minutes. Repeat inverting and cooking process several more times until both sides of crust are crisp and an even , deep golden brown.
Slide pancake onto a serving plate, season to taste with salt, and cut into wedges. Serve with grilled lamb chops.