1. Preheat your oven to 350°F. Line a baking sheet with parchment paper to prepare for the cookie dough.

2. In a small bowl, mix the softened butter, brown sugar, flour, cinnamon, and a pinch of salt until the mixture forms crumbly clumps. Chill the streusel while you make the cookie dough.

3. In a large bowl, cream the softened butter, neutral oil, and brown sugar until the mixture is smooth and creamy. Beat in the egg and vanilla extract. Then, stir in the cinnamon, baking soda, baking powder, and salt. Finally, add the all-purpose flour and mix just until a soft dough forms.

4. Scoop the cookie dough into balls, about 2 tablespoon each, and place them on the prepared baking sheet. Using your fingers, gently press a shallow well into the center of each dough ball.

5. Spoon the chilled streusel mixture into the wells of each cookie dough ball, pressing it down lightly so it adheres to the dough.

6. Bake the Gilmore Girls Coffee Cake Cookies for 10 to 12 minutes, or until the edges are set and the tops look dry. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

7. In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until the icing is smooth and pourable. Drizzle the icing over the cooled cookies, letting it drip down the sides for an extra-special touch.