For the brownies, preheat oven to 325F and grease an 8x8 inch baking pan.
Melt butter, chocolate and cocoa powder together in a medium saucepan, stirring until smooth.
Stir in sweetener and vanilla extract. Let cool 5 minutes.
Whisk in eggs, one at a time, until well combined, then whisk in sugar free Irish Cream.
Sprinkle with xanthan gum and whisk vigorously to combine.
Spread mixture in prepared pan. Bake 13 to 16 minutes, or until just barely set and middle is still not quite cooked (some readers have found they need to cook it longer - oven temperatures do vary). Watch them carefully as they can get quite dry if overdone. The edges will rise a little higher but should recede as they cool.
Let cool in pan.
For the frosting, beat butter and sweetener until smooth. Beat in sugar-free Irish Cream until well combined.