Line an 8-inch square pan with parchment and lightly oil the parchment. Stir the powdered sugar and cornstarch for the coating together and dust a little over the pan.
Combine the granulated sugar, 1 cup water, and lemon juice in a heavy saucepan. Bring to a boil without stirring, then cook until the syrup reaches 240 F on a candy thermometer.
Cook the starch mixture:
While the syrup cooks, whisk the cornstarch, 2 1/2 cups water, and cream of tartar together in a second saucepan until smooth.
Cook over medium heat, whisking constantly, until the mixture becomes very thick and translucent.
Slowly pour the hot sugar syrup into the starch mixture while whisking carefully. Reduce the heat to low.
Finish and set:
Cook over low heat for 45 to 60 minutes, stirring frequently with a heatproof spatula, until the mixture is deep golden, glossy, and pulls away from the pan.
Stir in the rose water, pistachios, and food coloring if using. Spread the mixture evenly in the prepared pan.
Let the Turkish delight set uncovered at cool room temperature for at least 8 hours or overnight.
Cut and coat:
Turn the set candy onto a board dusted with the coating mixture. Use an oiled knife to cut it into 36 cubes.
Toss every cut surface generously in the powdered sugar mixture and store the pieces between parchment layers.
Notes
A candy thermometer gives the most reliable texture.
Keep the final mixture over low heat and stir often to prevent scorching.
Store at cool room temperature; refrigeration can make the coating sticky.