Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a bowl, whisk together flour, baking soda, and salt; set aside.
In another bowl, beat shortening and sugar until creamy, then mix in mashed banana, eggs, and vanilla.
Gradually add dry ingredients to wet ingredients, mixing until combined.
Scoop tablespoon-sized portions onto the baking sheet, spacing them apart.
Bake for 10-12 minutes or until edges are lightly golden.
While cookies cool, mix glaze ingredients until smooth, then drizzle over cooled cookies.
Let glaze set for a few minutes, then enjoy!