Spritz a 9 by 5-inch loaf pan with water and line it with plastic wrap, leaving enough excess to fold over the top when filled.
Combine the gelatin and water in a 1-quart saucepan and set aside to bloom for 5 minutes.
Put the quark, cream cheese, anchovies, chives, and black pepper in the bowl of a food processor and process for 1 minute. Stop and scrape down the sides of the bowl.
Put the bloomed gelatin over low heat until melted, about 1 minute. Remove from the heat. With the food processor running, slowly pour the melted gelatin into the cheese mixture and process for 30 seconds.
Sprinkle the parsley evenly across the bottom of the prepared loaf pan. Pour 1/4 of the cheese mixture over the parsley. Top with 1/3 of the asparagus in a single layer, alternating direction of tips. Repeat with remaining cheese mixture and asparagus, ending with the cheese mixture. Fold the excess plastic wrap over the filling. Set a second loaf pan on top of the plastic wrap and press down to compact. Refrigerate until firm, about 2 hours.
Serve chilled, cut into 1-inch slices, along with crackers or toasted French bread slices.
To store, wrap in plastic wrap and refrigerate for up to 2 days.
Pour or spritz the water onto 4 paper towels. Spread out the paper towels and lay the asparagus on top of the dampened towels. Sprinkle with the salt. Roll up the asparagus in the dampened towels. Lay the bundle, seam side down, in the microwave. Microwave on high until the asparagus is just crisp tender, about 3 to 4 minutes. Remove from the microwave using tongs and carefully unwrap.