Combine all ingredients for the aioli together in a bowl. Cover and refrigerate until ready to use.
Heat 1/2 inch oil in a skillet until it reaches 350 degrees. If you don't have a thermometer, just drop a little batter in it and if it starts frying it's hot enough.
While oil is heating, whisk together flour, egg, ice cold water and a pinch of salt. Dip asparagus until batter. Turn to coat. Let excess batter drip off.
In batches, fry coated asparagus in oil until golden brown, 3 - 5 minutes. Turning occasionally. Transfer to a paper towel lined plate. Sprinkle with salt. Serve immediately with caper aioli.