1 pound slender asparagus, trimmed to 5-inch lengths, or a combination of 8 ounces asparagus and 8 ounces yellow or green zucchini, zucchini trimmed and cut on deep diagonal into 1/3-inch-thick slices, patted dry
For the sauce: Whisk the mayonnaise, capers, chives, tarragon, lemon juice, mustard, zest and garlic in a small bowl. Add 1/4 teaspoon hot sauce, or more, if desired. The sauce can be prepared 1 day ahead, covered and chilled.
For the asparagus: Whisk the flour, salt and pepper in a medium bowl. Whisk the beer into the flour mixture until smooth.
Pour enough vegetable oil into a heavy large wide saucepan to reach a depth of 3 inches. Attach a deep-fry thermometer to the side of the saucepan. Heat the oil over medium-high heat until the temperature registers between 350 degrees F and 360 degrees F.
Coat the asparagus, in batches, in beer batter, allowing any excess batter to drip back into the bowl. Drop the asparagus, in batches, into the hot oil and fry until the batter is deep golden brown and asparagus are crisp-tender, 2 to 2 1/2 minutes per batch. Adjust the heat as needed to maintain the oil temperature. Transfer the asparagus using a slotted spoon to paper towels to drain.
Immediately mound the asparagus on a serving platter. Place the bowl of dipping sauce alongside and serve while the asparagus are still hot.