Whisk together oats, flour, salt, cinnamon, and nutmeg. In another bowl cream together butter and sugars. Mix in milk and vanilla. Add dry ingredients to wet ingredients and mix until combined.
Mix together condensed milk and vanilla. In a large bowl whip heavy cream until stiff peaks form. Gently and gradually fold condensed milk into whipped cream. Once combined, stir in tablespoons of cookie dough.
Transfer mixture into 2 shallow containers. Cover and freeze for 8 hours or overnight.