Preheat oven to 350 degrees F. Grease a 9-inch springform pan and line the bottom with a circle of parchment; grease the parchment and set the pan aside.
Make the Strawberry Rhubarb Jam: In a small saucepan, stir together the cornstarch and sugar, then stir in the strawberries, rhubarb and water. Bring to a boil over high heat, then reduce heat to maintain a simmer and cook, uncovered, for 6 to 8 minutes, or until thickened, stirring occasionally. Remove from heat and set aside.
Make the Cream Cheese Filling: In a medium bowl, beat the cream cheese and sugar on medium speed until smooth, about 2 minutes. Add the egg and mix to combine.
Make the Cake Batter: In a large bowl, whisk together the flour and sugar, then cut in the butter until it is the size of small peas. Reserve ¾ cup. Stir the baking powder, baking soda, and salt into the remaining flour mixture. In a separate small bowl, whisk together the sour cream, egg, and vanilla extract, then stir into the flour mixture with a rubber spatula until thoroughly combined.
Spread the batter (it will be thick) onto the bottom and ½ inch up the sides of the pan. Spread the cream cheese filling over the batter, leaving a ½-inch border. Spoon the strawberry mixture in dollops over the top, then sprinkle with the reserved crumb mixture.
Bake until the edges are golden brown, 40 to 50 minutes. Cool for 20 minutes, then loosen the sides from the pan and cool completely before serving. Leftovers can be stored in the refrigerator for up to 4 days.