Combine the sugar, cream and water in a saucepan. Bring to a boil over medium heat, stirring until the sugar dissolves. Continue boiling for 15 minutes. While the liquid boils, melt the butter in a large, heavy pan over medium heat, then stir in the semolina and sesame seeds. Stir constantly for 15 minutes, making sure to scrape the bottom and sides of the pan so that the dry ingredients toast but do not burn.

When the liquid thickens, mix in the tahini, stirring well to break up any lumps. Pour this over the dry ingredients and stir well so that the liquid is well incorporated. Gradually add up to 1/2 cup of water to prevent sticking and help blend the ingredients. When this is done, turn off the heat and let the mixture sit for a few minutes. Turn the halvah out onto a flat surface and let it cool just enough so that you can work it with your hands. Knead well for several minutes. Transfer it to an 8x8" baking pan and smooth the top with a fork. Let it rest for 15 minutes, then loosen from the sides and bottom of the pan with a spatula, and turn it out onto a cutting board. Cut the halvah into 40 1x1-1/2" rectangles, and store in a tightly sealed container.