In a small bowl, combine 2 tablespoons brown sugar, 1/2 teaspoon cinnamon, 1/4 teaspoon ground ginger, 1/4 teaspoon kosher salt, and 1/8 teaspoon ground nutmeg. Set aside.: The moment you mix these dry spices you get a warm, nutty aroma that foreshadows the finished glaze. The blended scent of brown sugar and cinnamon is immediately noticeable, and you should see a uniform sandy texture. This preblend matters because it ensures even distribution on the fruit, preventing pockets of salt or spice. A common mistake is skipping this step and sprinkling ingredients separately, which can yield uneven flavor. If your sugar feels clumpy, break it up with a fork so it coats smoothly when it meets melted butter .
Cut 2 large peaches into quarters and remove the pits. For small peaches, cut into halves. Brush some of the 2 tablespoons melted unsalted butter over the cut sides of the peaches.: When you slice the peaches , you should notice the fragrant, fruity perfume escape, and the flesh will show tidy, juicy edges. Brushing with warm, melted butter adds a soft sheen and helps the sugar adhere. The butter also promotes browning and gives a toasty aroma as it heats on the grill. Avoid using cold butter because it will clump rather than spread, leaving dry patches that won't caramelize. Also, be careful removing the pits so you keep the fruit in intact wedges for easier grilling and flipping.
Preheat the grill or grill pan over medium heat. Make sure to clean the grill grates and grease with vegetable oil. Once the grill is hot, place the peaches cut side down and cook until grill marks are achieved, about 2 minutes. Grill the other cut side of the peach for 2 minutes.: A properly heated grill gives an immediate sizzle when the fruit touches the grates, and you will smell a toasty, slightly sweet steam rising. Watch for clear, dark grill marks that contrast with the soft flesh. That quick sear forms a bit of structure and concentrates flavor. One frequent misstep is grilling on too high a heat, which can blacken the surface before the interior softens; medium heat yields the best balance. Also, ensure the grates are clean so the fruit does not stick and tear when turned.
Flip the peaches over and sprinkle the surface with the brown sugar-spice mixture. Drizzle some of the melted butter on top to help melt the sugar. Cook until the sugar turns into a glaze and the peaches are soft, about 2 minutes. If desired, sprinkle on more brown sugar topping.: At this stage, you will hear a gentle caramelizing hiss and see the sugar begin to liquefy into a shiny coat. The aroma becomes deeper, a blend of toasted sugar and warm spices. Butter aids the process, helping the sugar form a thin, glossy film rather than dry granules. The sugar will start bubbling and then settle into a tacky glaze that clings to the fruit; that visual cue tells you it is nearly done. Avoid leaving them much longer because the sugar can burn quickly once it darkens past amber. If you notice smoke or a bitter scent, remove the peaches immediately and lower the heat.
Transfer the peaches to a serving dish and enjoy with a scoop of ice cream or serve with a salad.: When you lift the peaches off the grates, the softened flesh should yield easily to a fork and the glaze should still sparkle. The contrast of warm peaches with cold ice cream produces a pleasing temperature play, and the residual juices collect on the platter, adding flavor when spooned over. A common oversight is serving them too long after grilling, which leads to sogginess as the sugar absorbs moisture; serve promptly to preserve texture. If you need to wait, place them on a wire rack so steam can escape and the glaze stays slightly crisp.