Yea, I don't think EB without AB is a big deal, but it doesn't fit the concept.
I'm still debating some ideas, but the general idea (this is for an Eberron game) is a Brelish soldier who got caught in the Mourning. He woke up two years later in Sharn with no memory of any time since the Mourning happened. (Personally, I have no idea what happened in those two years, but it's a fun hook to throw to the DM.) He's been scraping by with odd jobs since then. What doesn't help is that weird things keep hanging around him whenever he's stressed or threatened. He gets jumped by a mugger and suddenly flames lash out and burn the attacker alive. (Hellish Rebuke). Or a field of cold surrounds him that freezes the hands of a guy who tried to start a bar fight with him. (Armor of Agathys) Or a fellow job-seeker gets tongue-tied during their job interview. (Hex on Charisma)
I'd probably rely on Greenflame or Booming Blade as his main attack, which I'd reskin depending on what domain and overall character flavor I plan on picking. Knowledge is my current favorite (lots of ghostly whispers from dead soldiers, refluff to psychic damage), but I also like the idea of a heavy armor build, maybe using Tempest, Life, or Zeal or Strength from Plane Shift: Amonkhet.