Position a rack in the center of the oven and heat the oven to 350°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.
Serve the oatmeal in wide, shallow bowls, topped with the pecan mixture.
To cut down on cooking time, you can soak the oatmeal overnight: Measure the coconut milk and water as instructed and then add the toasted oatmeal, 1 Tbs. sugar, and a big pinch of salt. Cover and refrigerate overnight. When you’re ready to cook, transfer everything to the saucepan, boil until the mixture begins to thicken, and then reduce to a simmer and cook until the oatmeal is tender and thick, 10 to 15 minutes total. Also, you can candy the pecans and coconut ahead of time, store in an airtight container, and stir in the peaches just before serving.