Line a 9 inch square pan with foil and spray with oil.
In a heavy saucepan over medium heat, combine 4 cups sugar, 1 1/2 cups of the water, and the lemon juice. Stir until the sugar dissolves and the mixture boils. Reduce the heat and simmer gently, without stirring, until the mixture reaches 240 F on a candy thermometer (soft ball stage.) Remove the pan from the heat and move onto step #3.
In a second heavy saucepan (larger than the first), stir together 1 cup cornstarch and the cream of tartar. Gradually stir in the remaining 3 cups of water until no lumps remain. Bring to a boil over medium-high heat, stirring constantly, until the mixture boils and is a thick, gluey paste. This happens very fast, don’t step away and don’t stop stirring!
Slowly pour the hot sugar, water, and lemon juice into the cornstarch mixture, stirring constantly. Reduce the heat and simmer, stirring often to prevent sticking, for about 1 hour, or until the mixture has become quite thick and slightly golden. It should be so thick that it drawing the stir spoon across the bottom of the pan leaves a trail that closes in slowly. You can test the texture of the product by dropping a blob into some cold water. It should be fairly solid and chewy, not runny.
) Stir in the flavoring and tint as desired with food coloring. Pour the mixture into the prepared pan and spread evenly. Cool to room temperature and let stand, uncovered, overnight to set.
) Sift the confectioners sugar and the remaining 1/4 cup cornstarch onto a large cutting board. Turn the Turkish delight out and cut into 1-inch squares with an oiled knife. Roll pieces in the sugar mixture to coat well. Store in an airtight container with sheets of waxed paper, dusted with the sugar mixture, separating every layer.