Line a fine mesh sieve with cheesecloth. Strain the horseradish for 2-3 minutes, or until reduced to 3/4 cup. Press on the horseradish with a spoon or squeeze the cheesecloth to extract all the liquid.
In a mixing bowl, whip the cream with a wire whisk until it thickens to the consistency of sour cream. You can use an electric mixer set on medium-high, but watch carefully so that the cream does not overwhip.
Add the horseradish, mustard, salt, pepper and Tabasco.
Whisk until thickened using a wire whisk or electric mixer. The sauce should be moist and the consistency of whipped cream.
Refrigerate for at least 1 hour, then serve immediately or transfer to a covered storage container and refrigerate up to an additional day.