Begin by washing the asparagus and trimming off the tough, woody ends. Cut the spears to a length that will allow them to stand upright in your canning jars.
Distribute the asparagus evenly between two 11 1/2 oz. canning jars, or a similar container. Add the thinly sliced shallot, garlic halves, and fresh dill sprigs among the spears.
In a medium saucepan, combine the distilled white vinegar, water, granulated sugar, and kosher salt. Place over medium heat and stir until the sugar and salt are fully dissolved, which should take about 1 minute.
Carefully pour the hot brine over the asparagus in the jars, ensuring the spears are completely submerged. Drop in the whole peppercorns for added flavor.
Allow the jars to cool to room temperature. Once cooled, seal the jars and place them in the refrigerator to chill overnight. This will allow the flavors to meld and the asparagus to pickle properly.
Your pickled asparagus will be ready to enjoy the next day and can be stored in the refrigerator for up to two weeks.