This dough spreads as it bakes, so be sure to leave plenty of room between cookies.
Preheat oven to 350 degrees. In a large bowl, combine butter, oats, sugar, apple, flour, cinnamon, and salt. Stir in eggs.
Drop dough by rounded tablespoons, 3 inches apart, onto parchment-lined baking sheets and gently flatten with damp fingers. Bake, one sheet on a time, until edges are golden, 10 to 12 minutes, rotating sheet halfway through. Let cool completely on sheets on wire racks.