Heat a wok until smoking hot. Add oil, then crab, tossing constantly 3 to 4 minutes until charred and bright red. Add garlic and ginger in the last 30 seconds. Remove crab.
Melt 1 tbsp butter over medium heat, add shallot, cook 1 to 2 minutes until softened.
Add the vinegar-stock mixture, scraping up browned bits, and simmer 1 to 2 minutes.
Add cream and simmer until reduced by half, 4 to 5 minutes, until it coats a spoon.
Remove from heat and whisk in remaining cold butter until glossy.
Stir in tarragon and season with salt and white pepper.
Return crab to the sauce, toss to coat, and warm through 1 minute before serving.