Line an 8-inch square pan with parchment. Dust the bottom with a mix of powdered sugar and cornstarch.
Combine sugar, 1.5 cups water, and lemon juice in a saucepan. Stir over medium heat until dissolved, then bring to a boil.
Cover the pot for 2 minutes to wash down crystals, uncover, then cook to soft-ball stage (about 240°F). Keep warm.
In a heavy pot, whisk 1 cup cornstarch with 2.5 cups water and cream of tartar until smooth.
Cook the slurry over medium heat, whisking constantly, until thick, glossy, and bubbling.
Slowly stream the hot syrup into the thickened slurry while whisking. Reduce heat to low.
Simmer gently 35–40 minutes, stirring often, until very thick and taffy-like and the mixture pulls from the sides.
Stir in rose water and the pistachios, if using, until evenly distributed.
Scrape the mixture into the prepared pan. Smooth the top and let it stand at room temperature until set, 4–6 hours.
Dust a board with powdered sugar and cornstarch. Turn out, cut into cubes, and toss to coat. Shake off excess.