Cranberry cake with cheesecake

Ingredients

• 450 grams (1 lb) cream cheese
• 80 grams (2.8 ounces) heavy cream (33%)
• 1 large egg
• 70 grams (2.5 ounces) powdered sugar
• 1 teaspoon lemon zest
• 100 grams (3.5 ounces) cranberries
• 50 grams (1.8 ounces) sugar
• 50 grams (1.75 ounces) water
• 6 grams (0.2 ounces) cornstarch
• 160 grams (5.6 ounces) butter
• 180 grams (6.35 ounces) sugar
• 120 grams (4.2 ounces) buttermilk
• 120 grams (4.2 ounces) milk
• 210 grams (7.4 ounces) flour
• 1 teaspoon baking powder
• 1/3 teaspoon salt
• 1 teaspoon vanilla extract
• 160 grams (5.6 ounces) cranberries
• 700 grams (1.54 lbs) cream cheese
• 300 grams (10.6 ounces) heavy cream (33%)
• 140 grams (4.9 ounces) powdered sugar