Preheat oven to 325°F. Turn the base of an 8-inch springform pan upside down so you can easily slide the cake onto a serving platter. Line the bottom with a round piece of parchment paper, then lightly spray the pan with vegetable cooking spray.
In a large mixing bowl, whisk together the flour, salt, baking powder, baking soda and granulated sugar. Make a well in the center and set aside.
In a small mixing bowl lightly whisk the eggs. Add the milk, melted cooled butter, and vanilla. Whisk until blended. The butter will be a little lumpy - this is fine.
Pour the milk mixture into the flour mixture and gently fold together with a spatula just until all of the flour is incorporated. The batter will be thick.
Transfer 1 ½ cups the batter to a clean bowl. Add 2 tablespoons coffee extract and 2 tablespoons Irish cream to the batter. Sift the cocoa powder over the batter and gently blend to combine.
Dollop scoops of the cake batter into the prepared pan, alternating between the two until all batter is used. Lightly draw a knife through the batter to swirl. Set the pan aside and allow it to rest for 15-20 minutes before baking. This step helps ensure good loft and puffiness.
Bake at 325°F until a toothpick comes out with no wet batter, about 45-50 minutes. Allow the cake to cool on a rack for 15-30 minutes.
Remove the sides of the pan and slide onto a serving plate. Mix the glaze ingredients together until smooth and drizzle over the cake. Cut into wedges and enjoy slightly warm or cooled. Store leftovers in a sealed container at room temperature for a day or two, or refrigerate for longer storage.