Trim asparagus and cut stalks diagonally into 1-inch lengths. Reserve tips separately.
In a large, heavy skillet, cook asparagus and onion in 3 tablespoons of the butter over medium-low heat until asparagus is tender, about 20 minutes. Puree asparagus mixture in a food processor until very smooth. If after pureeing the mixture you still have tough fibers, pass the mixture through a fine-mesh sieve before proceeding.
Preheat the oven to 325 degrees F and lightly coat the inside of 6 (1/2-cup) ramekins with the remaining tablespoon of butter.
Transfer the pureed asparagus mixture to a mixing bowl and whisk in the eggs, heavy cream, cheese, 1 teaspoon tarragon, salt and pepper. Divide the asparagus mixture evenly among the prepared ramekins and place ramekins in a large baking pan. Add enough hot water to come halfway up the sides of the pan, and bake, uncovered, until flans are set, about 25 to 30 minutes. Transfer the ramekins to a wire rack to cool slightly.
While flans are cooking, blanch the asparagus tips in a small saucepan of salted water until crisp-tender, about 3 minutes. Rinse under cool running water to keep from overcooking and set aside to drain. In a mixing bowl, whisk together the olive oil, lemon juice, chives, 2 teaspoons tarragon, lemon zest, Worcestershire Sauce, and salt and white pepper, to taste. Add the crabmeat and reserved asparagus tips and toss gently but thoroughly to combine. Reseason, if necessary.
When the flans have cooled slightly, run the tip of a paring knife around the edge of each flan and turn flans out onto serving plates. Garnish each flan with some of the crabmeat mixture and serve immediately. Flans are equally delicious served hot, warm, or at room temperature.
