Preheat oven to 350°F (175°C) and line a large baking sheet with parchment paper.
Prepare the streusel by mixing 1/4 cup flour, 1/4 cup brown sugar, and 1/2 tsp cinnamon in a small bowl; cut in 2 tbsp cold vegan butter with a fork until crumbly.
In a large mixing bowl, cream together the softened vegan butter, 1/2 cup brown sugar, and granulated sugar until light and fluffy.
Stir in the applesauce and vanilla extract until fully combined.
Whisk together 2 cups flour, baking soda, salt, and 1 1/2 tsp cinnamon in a separate bowl.
Gradually incorporate the dry ingredients into the wet ingredients until a thick dough forms.
Scoop approximately 2 tablespoons of dough per cookie and roll into balls, placing them 2 inches apart on the prepared baking sheet.
Use a thumb or the back of a spoon to create a shallow indentation in the center of each dough ball.
Generously fill each indentation with the prepared streusel mixture, pressing down slightly to adhere.
Bake for 10 to 12 minutes or until the edges are lightly golden and the centers are set.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.
Whisk powdered sugar and almond milk to create a glaze and drizzle over the completely cooled cookies.