Preheat oven to 350°F (175°C).
Prepare the crust: In a mixing bowl, cream together the butter and sugars until fluffy. Add flour, salt, and stir until combined.
Press the dough into an 8x8-inch baking dish to form an even layer.
Bake the crust for 15-20 minutes, or until lightly golden.
In another bowl, toss together the apples, lemon juice, cinnamon, nutmeg, and salt.
Spread the apple mixture evenly over the pre-baked crust.
Combine the oats and nuts (if using) with the remaining crust mixture and sprinkle over the apples.
Return the dish to the oven and bake for 25-30 minutes, or until the apples are tender and the topping is golden brown.
Remove from the oven and let cool before slicing into bars.
Serve warm or at room temperature, optionally with whipped cream or ice cream.