Prepare the syrup by simmering the sugar and water for 5 minutes. Add the rose water, saffron, cardamom, and lemon juice, then let it cool.
In a bowl, whisk together the eggs, milk, flour, and baking powder until smooth.
Mix the chopped walnuts, sugar, and cinnamon in a separate bowl.
Heat a lightly greased non-stick skillet over medium-low heat.
Pour half of the batter into the pan and cook for 2-3 minutes.
Sprinkle the walnut mixture evenly over the batter.
Pour the remaining batter over the filling and continue cooking.
Carefully flip the Khagineh and cook the other side until golden brown.
Transfer to a serving plate and cut into diamond or square pieces.
Pour the cooled saffron syrup over the warm Khagineh and let it absorb for 10-15 minutes before serving.