Slice the peaches into a medium bowl, then add the blueberries. Sprinkle the white sugar, vanilla, cornstarch, nutmeg and lemon juice on top, then gently stir everything together until it is all evenly coated. To ensure everything was mixed together gently, I just used my hands. Set aside the bowl.
Butter an 8 x 8 baking dish and preheat oven to 350ºF. In another bowl, mix together the rolled oats, flour, brown sugar, the other 1/8 teaspoon of nutmeg, and the salt. Add the butter and lemon juice and mix together with your hands until everything is uniform.
Pour the fruit into the baking dish and press down a bit to make the surface relatively even. Top with the rolled oats mix.
Bake until the topping is golden and the fruit juices are bubbling all around the edge. This will take around 28 minutes, depending on your oven's temperament. Let cool for a bit and serve, with vanilla ice cream or whipped cream, or, as my mom used to say, with nothing but a hungry mouth.