Heat the oven to 350 degrees F. Lightly butter an 8 by 8 inch or 9 by 9 inch baking dish, or a deep 9 inch pie plate.
Peel the apples, core them, and slice them about 1/4 inch thick. Drop the slices into a large bowl with the lemon juice and toss as you go so they do not darken.
Add the granulated sugar, 2 tablespoons flour, 1 teaspoon cinnamon, nutmeg, and 1/4 teaspoon salt to the apples and toss until the slices are evenly coated. Set aside while you make the topping.
In a second bowl, stir together the oats, 3/4 cup flour, brown sugar, 1/2 teaspoon cinnamon, and 1/4 teaspoon salt until combined.
Add the cold butter cubes. Rub the butter into the dry mixture with your fingertips, or cut it in with a pastry blender, until the mixture looks like coarse crumbs with some pea-sized buttery clumps. Do not overwork it into a paste.
Sprinkle the topping evenly over the apples, covering them completely to the edges. Press it down very lightly, just enough that it stays in place.
Bake for 40 to 45 minutes, until the topping is deep golden brown and the apple juices are bubbling thickly up around the edges of the dish.
Cool on a rack for at least 15 minutes before serving. This rest lets the filling set into a sauce instead of running. Serve warm, plain or with vanilla ice cream or softly whipped cream.