Start by heating your oven to 350°F (175°C). Prepare your cake pan by greasing it well and dusting it with flour, or just line it with parchment paper to make cleanup easier.
In a big bowl, sift together all your dry ingredients flour, cocoa powder, baking powder, baking soda, and salt so everything is well combined and light. Set this bowl aside for a moment.
In another bowl, mix the sugars with the wet ingredients. Whisk together granulated sugar, brown sugar, Greek yogurt, vegetable oil, eggs, and vanilla extract until the mixture is smooth and creamy.
Next, add the finely grated carrots to the wet ingredients and stir them in evenly. Now, slowly add the dry ingredients into the wet mix. Use a spatula or mixer on a low speed to combine them gently just mix until everything is incorporated, being careful not to overmix or the cake might get tough.
Pour the batter into your prepared pan, spreading it out evenly. Pop it into the oven and bake for about 35 to 40 minutes. You’ll know it’s ready when a toothpick inserted in the center comes out clean.
Once baked, let the cake sit in the pan for about 10 minutes to cool slightly, then transfer it onto a wire rack to cool completely before frosting.
While the cake is cooling, melt the mini chocolate chips gently in a saucepan over low heat or in short bursts in the microwave. Let the melted chocolate cool a bit so it’s not too hot when you add it to the frosting.
For the frosting, beat softened butter and cream cheese together until fluffy. Add the melted chocolate, some cocoa powder, vanilla extract, and powdered sugar, mixing well after each addition. Keep adding powdered sugar and a splash of heavy cream until the frosting reaches a creamy, spreadable texture.
Finally, once the cake is completely cool, spread the chocolate cream cheese frosting all over the top and sides.
Enjoy your cake! If you have leftovers, keep them refrigerated and take the cake out a little while before serving so it’s soft and delicious again.