Preheat oven to 350°F. Line a 9x13 baking pan with a piece of parchment paper (allowing the sides to hang over to easily remove the brownies once baked and cooled). Set aside.
In a large mixing bowl, stir together the brownie mix, eggs, oil, and water until smooth and completely combined. Do not overmix. Pour the batter into the prepared baking pan into an even layer.
In a medium-sized mixing bowl, using a handheld mixer on low, cream together the cream cheese and powdered sugar for 1 to 2 minutes or until smooth.
Add the vanilla extract, heavy cream, and all-purpose flour to the cream cheese mixture and continue to cream together for another 1 to 2 minutes.
Evenly dollop heaping spoonfuls of the cream cheese mixture randomly onto the brownie batter. Make sure to leave space between cream cheese dollops for the cherry pie filling.
Using the cherry pie filling, repeat step 5 and evenly dollop onto the brownie batter in between the cream cheese. You should still see some of the brownie batter also.
Using a butter knife, gently make swirls of the cream cheese mixture and the cherry pie filling. Make sure not to dip too deeply into the brownie batter layer. You want your cream cheese and cherry pie filling to remain as a top layer to these cherry cheesecake brownies.
Bake for 45 to 55 minutes or until the center is set and not jiggly. A toothpick inserted into the brownie portion should come out almost clean (you should not see raw batter). Do not overbake.
Cool your cherry cheesecake brownies in the pan, on the counter, then chill it in the refrigerator for at least 3 hours or up to overnight.