Beat butter and brown sugar together in a bowl using an electric mixer until smooth and creamy. Beat eggs and vanilla extract into creamed butter until incorporated. Mix flour, baking soda, salt, and cinnamon into creamed butter mixture until batter is just mixed; fold in oats and cinnamon chips. Drop batter, 1 to 2 tablespoons per cookie, onto a baking sheet.
Bake in the preheated oven until edges are lightly browned, 10 to 15 minutes.