In a heavy saucepan over medium heat, combine the apple juice, butter, sugar, salt, and cinnamon. Bring to a full rolling boil, stirring until the butter melts.

Add the flour all at once. Stir vigorously with a wooden spoon until it forms a shaggy mass.

Return to medium heat and stir constantly for 2 to 3 minutes, until the dough forms a smooth ball and leaves a thin film on the pan bottom.

Transfer to a bowl and stir 3 to 5 minutes until warm, not hot.

Beat in the eggs one at a time, fully incorporating each before adding the next. Add the fourth egg gradually, stopping when the dough is glossy and falls from the spoon in a slow V.

Fit a piping bag with a large open star tip. Pipe 2½-inch rings onto the parchment squares.

Transfer 4 to 5 squares into the preheated basket, not touching. Spray the tops lightly.

Cook at 350°F (177°C) for 12 to 15 minutes, until deep golden and firm. Do not open the basket before 12 minutes.

Cool on a wire rack for 10 minutes. Repeat with remaining dough.

Whisk the glaze ingredients until smooth and pourable. Dip each cruller face-down, return to the rack, and let set 15 minutes before serving.