Position a rack in the center of the oven and heat the oven to 350 degree F. Spread the oatmeal on a large baking sheet, pick through it for husks and pebbles, and toast in the oven until light golden brown and fragrant, about 12 minutes. Transfer to a large bowl to cool.

Line a baking sheet with parchment or a nonstick baking liner. In a small saucepan over low heat, combine 2 Tbs. of the sugar and the corn syrup, 1/2 tsp. water, and a pinch of salt. Cook over low heat, stirring occasionally, until the sugar is mostly melted (it won't dissolve completely), about 2 minutes. Off the heat, stir in the pecans and coconut. Spread the mixture in a thin layer on the prepared baking sheet and bake, stirring halfway through baking, until the coconut is dark brown, 16 to 18 minutes total. Transfer the pan to a wire rack to cool. Once cool, crumble the pecan mixture into a bowl and stir in the peaches.

While the coconut pecans bake, pour the coconut milk into a large liquid measuring cup and add enough water to make 4 cups. Transfer to a 4-quart saucepan, add the remaining 1 Tbs. sugar and a big pinch of salt, and bring to a boil over medium-high heat, whisking occasionally. Add the oatmeal and cook, whisking occasionally, until the mixture begins to thicken, about 5 minutes. Reduce the heat to low and simmer until the oatmeal is tender and thick, 25 to 30 minutes. Whisk occasionally at first and then switch to a wooden spoon and stir more frequently toward the end.