Combine white wine vinegar, water, sugar, and salt in a medium saucepan.

Bring to a boil, stirring until solids are dissolved.

Remove from heat and add tarragon and shallot.

Let stand for 5 minutes to infuse the brine.

Arrange asparagus in an even layer in a baking dish.

Pour brine over the asparagus.

Press paper towels against the surface to submerge the asparagus.

Let stand until cooled.

Transfer asparagus and brine to a large sealed container.

Refrigerate for up to 3 weeks.