Make the jam first. Cook the strawberries, sugar, and lemon juice for 5 to 7 minutes, gently mashing as they soften. Stir in the cornstarch-and-water slurry and cook for 1 to 2 minutes, until thick and glossy. Cool completely.
Build the dough. Mix flour, yeast, sugar, and salt. Warm the milk and buttermilk to about 110°F. Add the dairy, melted butter, eggs, yolk, and vanilla to the dry ingredients and mix until a soft dough forms.
Knead for 5 to 10 minutes by hand or with a mixer. Add flour gradually, stopping when the dough is smooth, elastic, and slightly tacky. Place it in a greased bowl, cover, and let it rise in a warm place for 1 to 1 1/2 hours, until doubled.
Prepare the cheesecake filling by beating 12 ounces cream cheese smooth, then adding sugar, vanilla, and a pinch of salt. Beat until fluffy.
Roll the dough into an 18-by-12-inch rectangle. Spoon or pipe the cheesecake filling across it, then swirl the cooled jam over the top. Leave visible streaks instead of blending the two fillings together.
Roll tightly from the long edge, trim the ends, and cut the log into eight even rolls. Set them in a greased 9-by-13-inch pan with room between them. Cover and let rise for 30 to 45 minutes.
Heat the oven to 350°F (160°C). Pour the 1/4 cup heavy cream over the rolls and bake for 25 to 35 minutes. They are ready when the tops are golden and the centers look set rather than wet.
For the icing, beat the remaining cream cheese and softened butter smooth. Add powdered sugar, vanilla, and enough heavy cream to make a spreadable glaze. Spread it over the warm rolls and finish with graham cracker crumbs.