In a medium saucepan, slowly whisk the chickpea flour into the water until completely smooth. Season generously with salt.
Cook over medium heat, stirring constantly, until the mixture becomes thick and begins pulling away from the sides of the pot, about 8-10 minutes.
Remove from the heat and stir in the chopped parsley.
Lightly oil a loaf pan and spread the mixture evenly inside. Let cool completely in the refrigerator, for a minimum of 1 hour.
Remove from the loaf pan and cut into thin slices, approximately ¼-inch thick.
Heat neutral oil to 350°F. Fry the panelle until golden brown and crispy on both sides.
Transfer to paper towels and season lightly with salt.
Pile the hot panelle onto a sesame roll. Finish with a squeeze of fresh lemon juice and serve immediately.