Yeah I actually forgot about the monk extra attack, haven't played a monk in awhile. But the more I look in to it, the more I see why you'd wanna go monk/sorc. Here is how I would play it. The only thing I'm conflicted with is either go open hand or elements with monk. Picker's choice I guess.
I would go as black dragonborn, kill Karlach for Infernal Robe from Mazora and have cold ancestry, it can be whatever ancestry you want, I'm just saying. That would be poison, fire, and cold resistance all at once. It looks pretty interesting.
Level 8 Monk, Level 4 Sorcerer
Stats
STR= 8 + (+2 Stat Potion)
DEX= 16 + (+4 Ability Improvement)
CON= 16
INT= 8
WIS= 15 + (+1 Hag Hair)
CHA= 10
Feats
Ability Improvement (+2 Dex)
Warcaster
Ability Improvement (+2 Dex)
Class
Sorcerer - Draconic Bloodline
Draconic Ancestry: (Choose Resistance)
Metamagic: Distant Spell
Metamagic: Extended Spell
Metamagic: Quickened Spell
Cantrips
Blade Ward
Ray of Frost
Fire Bolt
Shocking Grasp
Friends
Spells
Shield
Blur
Misty Step
Enlarge/Reduce
Mirror Image
I don't tend to favor sorcerer builds with low charisma, but I can see value in this approach.
I think I'd change the cantrips and the warcaster feat.
The low charisma is going to make the ray of frost and shocking grasp cantrips too weak to bother with. (Normally, I consider both of those to be S tier, but not here.) Firebolt could still be useful for exploding flameable items, smokepowder, surfaces, barrels, etc. As such, I'd replace ray of frost and shocking grasp with something more utility in nature, considering mage hand and minor illusion, perhaps.
The warcaster feat doesn't seem especially necessary. There's just enough concentration spells in the arsenal to warrant the expenditure of a feat. Instead, something like Alert would go a lot further, imo.
A part of me is questioning the metamagic choices, but with the abundance of scrolls, I suppose there'd be ample opportunity to use them.