Preheat your oven to 350°F (175°C). Gather your mixing bowls, measuring cups, and a lined baking sheet.

In a large mixing bowl, combine softened butter and vegetable oil with brown sugar. Beat on medium for 2-3 minutes until light and fluffy.

Add egg and vanilla extract to the butter mixture, continuing to beat well until fully incorporated.

Gradually sift in all-purpose flour, baking soda, baking powder, cinnamon, and salt. Mix on low speed until just combined.

Prepare the streusel topping by mixing softened butter, brown sugar, flour, and cinnamon together until crumbly.

Using a cookie scoop, drop rounded tablespoons of dough onto the baking sheet, spacing about 2 inches apart. Press lightly to create an indentation.

Bake for 10-12 minutes until lightly golden on the edges but still soft in the center.

While cooling, whisk together powdered sugar, milk, and vanilla extract for icing until smooth.

Allow the cookies to cool for 5 minutes before drizzling icing over each cookie.