Heat your grill to medium-high heat (around 400°F). While it preheats, cut four 12-inch squares of heavy-duty aluminum foil and lay them out on a clean work surface. This gives you time to prep while the grill reaches temperature, and having everything ready means you can work quickly once you start assembling.
In a small bowl, combine the light brown sugar, cubed unsalted butter, ground cinnamon, and kosher salt. Stir until the mixture is evenly combined and the butter starts to break down slightly from the warmth of the sugar. I like to do this step right before grilling so the butter stays cold and doesn't fully melt—it distributes better into the peach cavities this way.
Halve each of the four large ripe peaches and remove the pit from each half using a small spoon or melon baller—you should have 8 peach halves total. Divide the butter-sugar mixture from Step 2 evenly among the peach halves, pressing it gently into the cavity where the pit was. The mixture will melt as it cooks and create a sweet, caramelized sauce inside the foil.
Place two filled peach halves, cut-side up, on each foil square. Fold the foil up around the peaches to create a packet, sealing the edges tightly so steam stays trapped inside during grilling. I recommend folding the sides up first, then bringing the top and bottom together and rolling the edges over—this creates better steam retention than just crumpling them together.
Place the four sealed foil packets on the grill grate and cook for about 15 minutes total, rotating or moving them halfway through (around the 7-8 minute mark) to ensure even heating. The peaches will soften and the sugar will caramelize inside the packets while the foil protects them from direct flames. You'll hear a gentle sizzle, which means the butter and sugar are breaking down and creating that delicious sauce.
Remove the packets from the grill and let them sit for 2-3 minutes before carefully opening them (watch out for steam!). Flip each peach half so the cut-side faces down, nestling it into the caramelized sauce in the foil. Top each peach with a generous handful of honey-oat granola and a dollop of vanilla Greek yogurt, which will soften slightly from the warmth of the peaches and create a creamy contrast to the warm, caramelized fruit.