Add the raspberries to a medium saucepan over medium heat. Cook for 5-7 minutes, stirring and mashing occasionally, until the raspberries begin to break down and are liquidy.
Pass the raspberries through a sieve to remove the seeds.
Return the raspberry liquid to the saucepan, off the heat, and whisk in the cornstarch and sugar.
Heat the mixture over medium heat for about 10-13 minutes until the jam is thick.
To start, bloom your yeast. Mix your active dry yeast, sugar, and warm milk together and let sit for 10 minutes until foamy on top.
In a large bowl of a stand mixer with a whisk attachment, mix flour, salt and sugar together.
To the dry ingredients add the whisked eggs, vanilla, lemon zest and softened butter and mix.
Add in the yeast mixture and mix until everything is blended. Switch to a dough hook and knead on medium speed for 7-10 minutes until the dough pulls away from the edges of the bowl.
Form the dough into a ball. Place the dough in a large, greased bowl. Cover with plastic wrap or a kitchen towel and place in a warm place to rise for 1-1 ½ hours, or until the dough doubles in size.
While the dough rises, make the filling by mixing the butter, brown sugar, white sugar, lemon zest, lemon juice, salt and raspberry jam together in a small bowl.
Grease a 9×13" casserole dish and set aside.
Once the dough has had a chance to rise, punch the dough to release the air, remove it from the bowl and roll it out on a lightly floured surface.
Spoon the prepared lemon raspberry filling over the dough and spread it evenly.
Roll up the dough tightly into a long log shape starting from the end closest to you. Cut 12 rolls about 1 ½ inches wide.
Place the rolls in the greased casserole dish and pour room temperature heavy cream in between each roll. Cover them with plastic wrap and let them proof in a warm spot for about an hour.
Preheat the oven to 350 degrees F (175 degrees C) about 15 minutes before the rolls are done proofing.
Once the rolls have proofed, bake for 22-25 minutes, or until a light golden color.
While they bake, make the cream cheese frosting by adding the softened butter to a medium bowl and mixing it on high speed until pale and fluffy.
Add in the cream cheese and mix until combined.
Sift the powdered sugar into the mixture a little at a time and mix on low speed until all is combined.
Then add in the lemon zest and raspberry jam and combine until the frosting is fluffy.
Let the rolls cool for 5 minutes, then cover the warm rolls with the cream cheese icing.
