In a large saucepan, bring the honey, water, sugar, orange zest, cinnamon stick and lemon juice to a boil. Simmer over moderate heat until slightly thickened, 10 minutes. Discard the zest and cinnamon stick.

In a medium bowl, using a wooden spoon, beat the eggs with the olive oil and salt. Add the flour and stir until a stiff, shaggy dough forms. Turn the dough out onto a work surface and knead until smooth, about 2 minutes; add more flour if the dough is sticky. Cut the dough into 4 pieces, cover with plastic wrap and let stand for 20 minutes.

Roll 1 piece of dough at a time through a pasta machine, working your way from the widest setting to the thinnest. Transfer the dough strip to a well-floured work surface and dust with flour. Cut the strip into 4-inch squares. Repeat with the remaining dough.

In a large pot, heat 2 inches of vegetable oil to 360°F. Working with 8 squares at a time, roll each square into a loose cigar and drop it into the hot oil. Fry over moderate heat, turning once, until golden and crisp, about 3 minutes. Using a slotted spoon, transfer the pastries to a paper towel–lined baking sheet to drain. Repeat until all of the dough is fried.

Rewarm the honey syrup. Using tongs, add a few pastries at a time to the honey syrup and turn to coat. Transfer them to a large bowl and sprinkle lightly with chopped walnuts and cinnamon. Repeat until all of the pastries are coated. Carefully transfer the pastries to a serving platter and pour any remaining honey syrup on top. Serve right away.