Lightly grease an 8x8-inch metal pan with neutral oil or cooking spray. Line it with baking parchment, then lightly grease the parchment as well. Set aside.

In a medium saucepan, combine the sugar, lemon juice, lemon zest, and 1½ cups of water. Place over low heat and stir gently until the sugar fully dissolves. Increase the heat to high, cover the saucepan, and bring the mixture to a boil for 5 minutes to dissolve any sugar crystals that may have formed along the sides. Uncover, insert a candy thermometer, and continue boiling until the temperature reaches between 240°F and 250°F. The syrup should be slightly golden in color at this stage.

While the sugar syrup is cooking, combine the cornstarch, cream of tartar, and 2 cups of water in a deep saucepan. Whisk continuously over medium heat until the mixture thickens into a smooth, glossy paste, approximately 3–5 minutes. Remove from heat and set aside.

Once the syrup reaches the correct temperature, carefully pour it into the cornstarch paste in small increments while whisking to avoid lumps. Return the pan to low heat and stir until fully combined and smooth.

Increase the heat briefly until the mixture begins to bubble, then reduce it to low and cook gently for approximately 1 hour. Stir frequently using a wooden spoon to prevent sticking. The mixture is ready when it becomes thick, glossy, and pulls away from the sides of the pan.

Remove the mixture from heat and immediately stir in the rose water, vanilla extract, and food coloring (if using). Mix thoroughly until evenly incorporated.

Carefully pour the hot mixture into the prepared pan, smoothing the surface with the back of an oiled spoon or spatula. Allow the Turkish delight to set uncovered in a cool, dry area overnight, for at least 12 hours.

The next day, sift together the powdered sugar and cornstarch in a large bowl. Lightly dust a clean surface with this mixture. Invert the Turkish delight onto the surface and peel away the parchment paper. Sprinkle more of the sugar-cornstarch mixture over the top. Using an oiled knife or pizza cutter, slice the candy into 1-inch squares, tossing each piece in the sugar mixture until evenly coated.

Serve immediately or store the Turkish delight in an airtight container at room temperature. Layer the pieces with parchment paper and a light dusting of the sugar-cornstarch mixture to prevent sticking.