Reduce the oven temperature to 325℉.
In a large bowl, add the cream cheese, sugar, and flour. Use a hand mixer to combine on med-low speed until the mixture is smooth, 30-40 seconds.
16 oz cream cheese, ⅔ cup sugar, 1 ½ tablespoon flour
Add the eggs one at a time, mixing on low until just combined. After each addition, use a rubber spatula to scrape the sides and bottom of the bowl well.
2 eggs
Add the vanilla, sour cream, and heavy cream. Combine on low until just combined, scraping the bottom and sides of the bowl again.
1 teaspoon vanilla, ¼ cup sour cream, ¼ cup heavy cream
Divide the batter evenly into the 12 cupcake liners. A large cookie or muffin scoop makes this easier. Each liner should be almost full.
Optional: If swirling, add about 1 teaspoon of the reserved topping to each and use circular motions with a toothpick to move it gently towards the edges. It doesn't need to go all the way - it will continue to spread while it bakes.
Bake the cheesecakes at 325℉ for 18-20 minutes, or until the centers just barely jiggle. Be careful not to overbake.
Cool fully at room temperature for 1-2 hours, then place in the fridge uncovered to chill for 2-3 more hours, or overnight. When it's time to serve, warm the remaining blackberry sauce gently in the microwave. Then serve on top of the cheesecakes.