Oatmeal Cookie Sandwiches with Nectarine Ice Cream

Cookies

• 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

Ice Cream

• 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