Start by soaking mustard seeds in rice wine vinegar for five hours, preferably overnight.

Sweat shallots over medium-high heat with a pinch of salt and oil.  When the shallots become translucent, deglaze with the wine.  Reduce until the shallots are almost dry.  Remove from the heat and cool. 

Strain the hydrated mustard seeds and reserve two tablespoons of the vinegar.  To a food processor add aioli, the plumped mustard seeds, horseradish, chives, the sweated shallots, and the reserved vinegar.  Blend, then season with salt and pepper.