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Preheat the oven to 400u00b0F (200u00b0C/Gas Mark 6) and grease 2 cookie sheets (baking trays) with butter. Sift together the flour and salt into a large bowl and make a well in the center. Add the sugar, oil, lemon zest, and vanilla. Stir the baking soda into 5 tablespoons water in a bowl and pour into the well. Using a spoon, gradually incorporate the dry ingredients, then knead gently to a soft and pliable dough, adding a little more water if necessary. Break off small pieces of dough and roll into cylinders the size of your thumb, then press lightly to flatten. Put them onto the prepared baking sheet, spaced well apart, and bake for 20-25 minutes, or until lightly golden. Remove from the oven. To make the syrup, put the sugar, honey, and 1 1/4 cups (300 ml / 1/2 pint) water into a pan and bring to a boil. Boil for 5 minutes, then remove from the heat. Pour a mixture of equal parts olive and corn oil into a heavy pan to a depth of 3 inches (7.5 cm) and heat it to 375u00b0F (190u00b0C), or until a cube of bread browns in 30 seconds. Carefully drop batches of the cookies into the hot oil and fry for a few minutes, until golden brown. Remove with a slotted spoon, drain well, and drop into the hot syrup. Let absorb syrup for 3-4 minutes. Remove with a slotted spoon, transfer to a serving platter, and sprinkle with finely chopped walnuts.
