Preheat the oven to 350 degrees F (180 degrees C) and grease a 9-inch round springform pan liberally with butter or shortening.
Prepare the red velvet brownie batter first. Fill a small pot halfway with water and bring it to a gentle boil on the stove.
Combine the All-Purpose Flour (1/2 cup), Baking Powder (1/4 teaspoon), and Salt (1/4 teaspoon) in a bowl and mix it together. Set it aside.
Combine the sliced Butter (5 tablespoon) and Semi-Sweet Chocolate Chips (4 ounce) in a heat proof bowl and set it over the simmering water. Let it melt as you gently stir it with a heat proof rubber spatula. Once it is smooth and shiny, take the bowl off of the heat.
Let it cool for a minute, then whisk in the Dark Brown Sugar (1/2 cup), followed by Egg (2) and Red Food Coloring (1 fluid ounce).
Lastly, whisk in the dry ingredients just until they disappear and the batter is smooth. Set the batter aside.
Next, prepare the cheesecake batter. Set up a stand mixer with the paddle attachment. Combine the Cream Cheese (8 ounce) and Greek Yogurt (1/4 cup) in its bowl and beat them together until smooth and fluffy.
Add in the Granulated Sugar (2/3 cup) and Vanilla Extract (1 tablespoon) and let them get mixed in well.
Pour in remaining Egg (2) one at a time and let them get mixed in well too. Finish with the All-Purpose Flour (1 tablespoon) and let it all get well combined and smooth. Set the batter aside.
Take the brownie batter and reserve a 1/4 cup. Pour the rest into the greased cake pan and smooth it out into a thin, even layer.
Take the reserved 1/4 cup of brownie batter and drizzle it all over the cheesecake layer. Use a butter knife to gently swirl it into the cheesecake batter.
Bake the cheesecake brownies for about 30 minutes, until set and baked through. The cheesecake will just start to get golden around the edges.
Take it out and let it cool for 30 minutes before releasing it from the springform pan. Sprinkle the top liberally with Red Crystallized Sugar (to taste)) for some extra sparkle.
Transfer it to a cake plate with a dome to seal it and let it refrigerate for at least 3 hours or up to overnight.
Grab a heart shaped cookie cutter that's about 2-3 inches wide at the widest part. Cut out heart shaped brownies as close together as possible to yield as many brownies as you can.
Serve them immediately for a sweet, romantic treat! Serve and enjoy!