To make the oat crumble, combine all the ingredients together in a large mixing bowl and mix well.
Transfer the mixture to a sheet pan lined with parchment paper and bake for 7-10 minutes until fragrant and golden brown.
Remove from the oven and allow to cool for 10 minutes before serving with the peaches.
Any leftover crumble can be stored in an airtight jar for up to 2 weeks.
Halve the peaches carefully with a sharp knife then twist to separate the two halves.
Remove the stones/pits and discard.
Brush the peach halves with melted butter then place, cut-side down, on hot grill grates (or use a grill pan set over medium heat).
Allow the peaches to cook for 8-10 minutes until caramelized with grill marks and starting to soften.
I don't add any sweetener to the peaches before grilling as I prefer their natural sweetness but you could add a sprinkle of brown sugar to them before grilling.