Combine the water, butter, sugar, and salt in a saucepan over medium-high heat. Bring to a full boil, add flour all at once, and stir vigorously for 2 minutes until the dough pulls into a ball and leaves a film on the pan.

Transfer dough to a mixer bowl, cool 3 to 4 minutes, then beat in the eggs one at a time on medium speed until the dough is smooth, glossy, and falls in a thick ribbon.

Cut 12 parchment squares (about 3 inches each), fit a piping bag with a large open-star tip, and pipe 3-inch rings onto each square.

Heat neutral oil to 375°F (190°C) in a heavy pot. Lower crullers in parchment-side up, remove parchment after 30 seconds, and fry 3 to 4 minutes per side until deep golden brown. Rest on a wire rack for 5 minutes.

Whisk the sifted powdered sugar, honey, 3 tbsp milk, and vanilla together until smooth. Adjust consistency with the remaining milk if needed.

Dip each cruller face-down into the glaze, lift, and set glaze-side up on the wire rack for 5 minutes to set. Transfer to a serving plate.