Measure out water in a small bowl and add ground flax seed. Stir and let sit for 10 or so minutes. The mixture should thicken up and become egg-like in consistency.
In a bowl, mix all ingredients except for hot fudge. Pour into a microwave-safe mug, taking care not to fill mug more than half-way. Microwave on full power for one minute. Remove and drizzle hot fudge over top. Serve immediately.
Don't grease the mug!
Recipe for Irish Cream Chocolate Mug Cake found here: https://www.mysequinedlife.com/irish-coffee-chocolate-mug-cake/