Preheat oven to 350 degrees F. Line a 8×8 inch square pan with parchment paper.
In a medium bowl, make the flax eggs by adding the ground flaxseeds and water. Stir until combined. Set aside for 5 minutes to thicken.
In a large bowl, add the flour, cacao powder, baking soda, and salt. Whisk until well combined.
In the bowl with the flax eggs, add the chocolate cream cheese, coconut oil, sugar, vanilla, and almond milk. Whisk until combined.
Add wet to dry. Use a spatula to mix until just combined. Don’t over mix. Fold in chocolate chips. The batter will be very thick.
Make the strawberry cheesecake swirl by adding the strawberry cream cheese, sugar, milk, and cornstarch to a bowl. Mix with a spoon until well combined and smooth.
Add 2/3 of the brownie batter to the lined pan. Spread batter out evenly in the pan. Drop spoonfuls of strawberry cheesecake batter over the brownie batter. Then drop spoonfuls of the leftover 1/3 brownie batter in the empty spaces between the cheesecake filling. Use a knife and gently swirl the batters together.
Bake for 35-40 minutes until center is set. Don’t over bake. It will firm up more when it cools. Cool brownies in the pan on a wire rack and then place in the fridge for a few hours or overnight. Slice and enjoy!