In a medium bowl, stir the golden syrup, oil, and food-grade lye water until smooth and evenly combined. Add the flour and stir with a spatula until no dry flour remains. Gently knead just until the dough comes together; do not overwork it. Cover the bowl and let the dough rest at room temperature for 30 minutes.
Meanwhile, divide the red bean paste into 8 equal portions, about 1 ounce (30 g) each. Roll each portion into a smooth ball. If the paste is sticky, chill it for 10 to 15 minutes to make shaping easier.
Divide the rested dough into 8 equal portions, about 1 ounce (32 g) each. Keep the portions covered with plastic wrap or a clean, barely damp towel so they do not dry out.
Lightly flatten one dough portion into a 3-inch round, keeping the center slightly thicker than the edges. Place one red bean paste ball in the center. Gently push the dough up around the filling, pinching the seam closed. Roll lightly between your palms until smooth. Repeat with the remaining dough and filling.
Lightly dust a 50-gram mooncake mold and each filled ball with flour, tapping away excess. Place one ball on a parchment-lined baking sheet. Press the mold firmly over the ball, then lift straight up to release the patterned mooncake. Repeat with the remaining cakes. If you do not have a mold, gently flatten the filled balls into thick rounds and press a simple pattern on top with the tines of a fork.
Preheat the oven to 350°F (175°C). Bake the mooncakes for 5 minutes. While they bake, whisk the egg yolk and water together until completely smooth.
Remove the baking sheet from the oven. Let the mooncakes cool for 10 minutes, then brush them very lightly with a thin coat of egg wash. Avoid letting egg wash pool in the pattern. Return them to the oven and bake for 10 to 12 minutes more, until lightly golden brown.
Cool completely on the baking sheet. For the softest, classic-style crust, store the cooled mooncakes in an airtight container at room temperature for 1 to 2 days before serving; this resting period lets the crust soften and develop a deeper color.