Place peaches (about 1 1/2 cups) in your mug and set aside for a few seconds to shaw peaches if they're frozen.
In a small bowl, whisk flour, instant oats, rolled oats (if you want a slightly oat-y cobbler), brown sugar, and a few dashes of ground cinnamon (about 1/8 tsp), and a light dash or two ground nutmeg, until combined. Then stir in nondairy milk.
Place the oat mixture on top of the peaches and microwave 1-2 minutes, until the oat topping has cooked and looks a little like oatmeal. Top with yogurt and serve.