Cut the top 2 to 3 inches from each asparagus stalk; reserve the bottoms for another use.

Fill a large bowl with ice water. Bring a pot of salted water to a boil. Add the asparagus tops and cook until bright green, 2 to 3 minutes. Drain and plunge into the ice water, then drain well and transfer to a blender; set aside.

Whisk the egg yolks and sugar in a medium bowl. Heat the milk and cream in a saucepan over medium heat until it just boils. Remove from the heat and gradually add the yolk mixture, whisking constantly. Return the pan to the heat and cook, stirring constantly with a wooden spoon, until the custard is thick enough to coat the spoon and a thermometer registers 170 degrees F, about 10 minutes (do not let the custard boil).

Transfer the custard to the blender with the asparagus and puree until smooth, 1 to 2 minutes. Cool completely, then strain through a fine-mesh strainer.

Freeze the asparagus custard in an ice cream maker according to the manufacturer's instructions. Use two spoons to shape the ice cream into quenelles (oval-shaped scoops).