In a medium saucepan combine the ingredients for the syrup. Bring to a boil, reduce heat to low and then simmer, covered, for approximately 5 minutes. Remove from heat and let cool. After the syrup has cooled, remove the apple core, apple peel and cinnamon sticks.
In a large pot heat the olive oil and the semolina over medium heat. Stir well and cook, stirring constantly until the semolina starts to brown slightly and smells toasty. Add the grated apple to the pot and cook for an additional minute. Move pot off of the burner for the next step.
Very carefully, add the syrup to the pot with the semolina and oil. It will likely splatter a little bit, so be very careful and be sure that there are no children or pets near the oven. Once all of the syrup has been added, return the pot to the heat. Reduce heat to low-medium.
Stir constantly. The mixture will thicken and begin to pull away from the sides of the pot as you stir. Watch video here. When it has reached this consistency, remove from the heat and transfer approximately 1/3 of the semolina mixture to the pot which used to contain the syrup. Add in the raspberry jam and stir well until it is totally combined. Your semolina will turn a lovely pink colour.
Ladle the semolina into a slightly greased mold like a bundt pan or a jell-o mold. First, ladle in 1/2 of the plain apple semolina, then the raspberry semolina, and then top with the rest of the plain apple semolina.
Let the halva cool and then refrigerate it for at least one hour. Remove from the mould and cut into serving pieces.