Place potatoes in a large pot then cover with at least 2" of cold water. Add salt then bring water to a simmer over high heat. Reduce heat to medium-low and cook about 40–45 minutes until tender but still firm. The potatoes must be cooked through, but still firm enough to hold their shape.

Drain water and allow potatoes to cool until they can be handled. Cut each potato in half lengthwise, then continue cutting lengthwise into 1"-thick wedges.

Preheat outdoor grill to medium-high or an indoor grill to high heat. Spray potato wedges generously with cooking spray then season all sides with garlic salt and grill until golden brown marks appear and potatoes are heated through—about 2 to 3 minutes per side on outdoor grill and about 8 minutes per side on indoor grill.

Transfer to a serving platter then sprinkle with pepper and Parmesan cheese. Serve immediately.