Set your oven rack to the middle position and preheat to 350°F (175°C). Lightly butter the inside of a 9x13 inch (23x33 cm) baking dish and set it aside.
Peel all 6 apples, then core them and slice into pieces about ¼ inch (6 mm) thick. Place the slices directly into your large mixing bowl as you go.
To the apples, add the granulated sugar, 2 tablespoons brown sugar, cornstarch, lemon juice, 1 teaspoon cinnamon, nutmeg, and ¼ teaspoon salt. Toss gently until every slice is coated and no dry cornstarch remains.
Tip the seasoned apples into the buttered dish and spread them into an even layer. Press them down lightly and scrape in any sugar and juice left in the bowl.
In your medium bowl, stir together the oats, flour, ¾ cup brown sugar, ½ teaspoon cinnamon, and ¼ teaspoon salt. Cut in the cold cubed butter with a pastry blender until clumps form, then stir in the nuts if using.
Scatter the topping evenly over the apples, leaving some larger clusters intact. Do not pack it down, then bake for 40 to 45 minutes until deep golden and bubbling at the edges.
Transfer the dish to a wire rack and let it rest for at least 15 minutes so the cornstarch can finish thickening the juices. Serve warm, ideally with vanilla ice cream.