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If you are playing Monk which calculates unarmed damage using DEX, then the result would be something like Damage Roll + DEX Mod(Proficiency) + STR Mod(Tavern Brawler)
So is it Dex + 2x Str?
This is incorrect. It'll use whichever value is highest, taking into account the TB bonus. If you read carefully, the Monk's feature says it'll use Dexterity instead of Strength only if it is higher.
It'll be Damage Roll + Proficiency Bonus + (Highest between STR*2 and DEX). If your Dexterity modifier is higher than twice your Strength modifier, such as if your Dexterity is at 16(+3) and your Strength is at 12(+1), it'll use the Dexterity normally. Otherwise, it'll use Strength.
Assuming an Unarmed Attack with a Monk, it should look like this.
Damage Roll + STR/DEX Mod(Whichever is higher) + STR Mod(Tavern Brawler).