Oatmeal Cookie Sandwiches with Nectarine Ice Cream

Name: Oatmeal Cookie Sandwiches with Nectarine Ice Cream
Ingredients: 1 1/2 cups old-fashioned oats; 3/4 cup all purpose flour; 1/2 teaspoon baking soda; 1/2 teaspoon ground cinnamon; 1/2 teaspoon salt; 1/2 cup (1 stick) unsalted butter, room temperature; 1/3 cup (packed) dark brown sugar; 1/3 cup sugar; 1 large egg; 1/2 teaspoon vanilla extract; Nonstick vegetable oil spray; 1 1/2 pounds nectarines, pitted, cut into 1/4-inch cubes; 1/4 cup sugar; 1 pint vanilla ice cream, softened slightly