Heat oil in a low-sided 6-quart saucepan over medium-high heat until a deep-frying thermometer registers 360 degrees. Cut thirty 4-inch squares out of parchment. Line two baking pans with paper towels.

Meanwhile, sift the flour into a medium bowl. In a medium saucepan, combine the milk, salt, sugar, and butter. Bring to a full boil over medium-high heat. Remove from heat; add the sifted flour, all at once, stirring constantly until flour has been incorporated. Return to heat; cook, stirring constantly, until the dough pulls away from sides, about 30 seconds. Remove pan from heat.

Transfer dough to bowl of an electric mixer fitted with paddle attachment. Beat on low speed until the bowl is warm to the touch, 4 to 5 minutes. Add eggs, one at a time, beating until each egg has been incorporated before adding the next. Stir in poppy seeds.

Coat a baking pan with cooking spray, spread 5 squares of parchment on top, and generously spray parchment. Fit a large pastry bag with a #4 star tip; fill with dough. In one continuous stroke, pipe a 2 1/2-inch double-layer circle onto each square.

Carefully lifting squares, gently slide 5 doughnuts into oil. Cook until golden brown, about 2 minutes. Using a slotted spoon, turn over; continue cooking until evenly browned, about 2 minutes more. Transfer to lined baking pans; let rest until cool enough to handle.

Repeat steps 4 and 5 with remaining parchment squares and dough.

Coat doughnuts with lemon glaze. Sprinkle with lemon zest and a pinch of poppy seeds. Transfer to a wire rack to set; serve.