Improved Unarmed Strike, Monk HTH progression, and +1 CL advancement (in specific for a Sorcerer) + whatever if there is more, no biggie if not.
Is there any class or PrC that can supply this with a one level dip?
Improved Unarmed Strike is a feat that can be applied regardless of a dip, though the Monk Unarmed Damage progression is a hard-based class feature that requires levels in either Monk or Brawler, or very high levels in Rogue/Ninja and to select a specific talent. No, not even Warpriest would work, because they canned the progression on that. The only other option is with a Monk's Robe, and that only puts you at 5th level progression (or 1D8 damage).
The Sorcerer Caster Level advancement can't be fixed except by prestige classes that enhances a single arcane class's spell progression, and I can assure you that there are none which do that and offer the same benefits you want.
At best, you can continue to take Sorcerer levels and pick up a Monk's Robe and the Improved Unarmed Strike feat. At worst, you're only ever going to improve two of the three at any given time, and even that varies based on what two you choose.
"Esoteric" Magus Archtype is the closest I can think of that'd help you.