In a medium bowl, whisk together the flour, brown sugar, and cinnamon
Add the cold cubed butter and use a pastry cutter or two butter knives to incorporate the butter until only pea-sized pieces remain.
Place in the fridge until ready to use.
For the cookies:
Preheat the oven to 350°F (180°C), or 160°C for a fan oven. Line 2 baking sheets with parchment paper and set aside.
In a large bowl, whisk together the flour, cornstarch, baking soda, baking powder, and salt; set aside.
In a separate large bowl, cream the butter and brown sugar until smooth, 2-3 minutes. Add the egg and vanilla and mix well.
Add the flour mixture and mix until just combined.
Use a small cookie scoop, 1.5-2 tablespoons, to drop dough onto the prepared cookie sheets. Use a 1-1.5 teaspoon measuring spoon to create an indentation on the cookie dough balls.
Fill the indentation with 1 tablespoon of crumble mixture.
Bake in the preheated oven for 8-10 minutes, or until the cookies are lightly golden. Allow to cool completely.
For the drizzle:
Whisk together the powdered sugar and milk in a medium bowl until smooth. Drizzle over the cooled cookies and allow to sit for at least 5 minutes.
Notes
Adjust the Glaze: You might mix up the ingredients and find that the icing is a bit too thin or too thick for drizzling. That's ok, and easy to fix! Add more milk to thin it out, or more powdered sugar to make it thicker.
Let the Cookies Cool: You don't want to add the glaze to warm cookies, or it will melt and soak in. Be patient and let these tasty coffee cake cookies cool down completely before adding the icing.
To Store: Once cooled, you can store these cookies in an airtight container at room temperature for up to 3-5 days. I suggest keeping them in a single layer, as the icing can soften and the cookies might stick together.