Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a large bowl, cream together the softened butter, vegetable oil, and brown sugar until light and fluffy. Add the egg and vanilla extract, blending until incorporated, then fold in cinnamon, baking soda, baking powder, salt, and flour until just combined.

In another bowl, mix softened butter, brown sugar, flour, cinnamon, and salt for the streusel topping until it resembles coarse crumbs.

Scoop tablespoons of dough onto the prepared baking sheet, spacing them 2 inches apart. Create a small indent in the center of each scoop and fill with streusel topping.

Bake for 10 to 12 minutes, until the edges are golden and centers are set. Avoid overbaking.

Let the cookies cool on the sheet for a few minutes before transferring to a wire rack. Whisk together powdered sugar, milk, and a splash of vanilla extract for icing.

Once cooled, drizzle icing over each cookie and sprinkle with cinnamon or turbinado sugar if desired.